McAleny joined Everton as an 11-year-old and made his debut for the club's youth team in a 1–0 Premier Academy League win over Tottenham Hotspur on 25 August 2007, replacing Lewis Codling after 65 minutes. McAleny became a full-time member of the club's academy in 2008, at age 17. He made regular appearances for the youth team during the 2008–09 season and received his first call up to the reserve team for a Premier Reserve League North match against local rivals Liverpool on 17 February 2009. McAleny remained on the bench for the 1–1 draw. McAleny broke into the reserve team during the 2009–10 season, making his debut in a 1–0 defeat to Manchester United on 6 October 2009, replacing Jose Baxter after 61 minutes. McAleny's form for the youth and reserve teams saw him awarded his first call into the first-team squad for a dead rubber Europa League group match versus BATE Borisov on 17 December 2009. Awarded the number 40 shirt, McAleny was named on the bench in a youthful squad, but did not make an appearance in the 1–0 defeat. McAleny finished the 2009–10 season with 26 appearances and 12 goals for the youth team.
McAleny received his first call up for a Premier League match versus Aston Villa on 2 April 2011. Awarded the number 31 shirt, he remained on the bench for the 2–2 draw and was included in the squad again for a 3–0 victory over Wolverhampton Wanderers in the following game. McAleny made his first-team debut as a second-half substitute for Phil Neville in a 1–0 league defeat away to Arsenal on 10 December 2011, nearly scoring with a volley. He made his first home appearance in the following game, coming on for Louis Saha in a 1–1 draw against Norwich City. McAleny's final call into the first-team squad of the 2011–12 season came in a 2–0 FA Cup third round victory over Tamworth at Goodison Park on 6 January 2012. McAleny signed a new two-year contract in the summer of 2012. No longer eligible for the youth team, McAleny played exclusively for the reserve team during the 2012–13 season, though ankle and ligament injuries hindered his progress. After spending much of the first half of the 2013–14 season out with a broken leg, McAleny received his first call into the first-team squad in over two years, when he was named as a substitute for an FA Cup fourth round tie versus Stevenage on 25 January 2014. He remained on the bench for the 4–0 victory. He also returned to reserve team action, scoring three goals in two games in March. Having come to the end of his contract, McAleny was offered a new deal at the end of the 2013–14 season. On 1 July, it was announced that McAleny had signed a new three-year contract, after being assured he was part of manager Roberto Martínez's plans.
On 23 March 2012, McAleny joined League One side Scunthorpe United on loan for the remainder of the season. He made his debut the following day, coming on as a 65th-minute substitute for Jordan Robertson in a 0–0 home draw with Notts County. A knee injury saw him make just three appearances for the club.
On 25 July 2013, McAleny joined League One side Brentford on loan until 6 January 2014, linking up with former Everton teammates Adam Forshaw and Jake Bidwell. On 24 August, in only his fourth appearance for the club, he broke his leg in a clash with Walsall's Adam Chambers. On 2 September, Brentford announced that the loan arrangement had been brought to an early end, as McAleny was expected to miss most of the 2013–14 season. Brentford manager Uwe Rosler said that Conor would be "a big miss, he would be welcome back any time". McAleny attracted further transfer interest from the Bees in March and June 2014.
On 2 February 2015, McAleny joined Championship side Cardiff City on loan until the end of the season. On 3 March he scored his first professional goal, in a 3–1 win at Rotherham United. He scored again on 4 April, set up by Aron Gunnarsson, to equalise in a 1–1 draw against Reading at the Madejski Stadium.
On 14 September 2015, McAleny joined Championship side Charlton Athletic on loan until 7 November 2015. The next day, he made his debut for the club as a 74th-minute substitute replacing Morgan Fox in a 2–1 home defeat to Huddersfield Town. On 23 September 2015, he made his first start in a 4–1 Capital One Cup away defeat to Crystal Palace. He was replaced by Tony Watt in the 75th minute. However, on 5 November 2015, two days before the end of his loan contract, he was sent back to Everton after not scoring in his short spell.
On 1 February 2016, McAleny joined League One side Wigan Athletic on loan for the until the end of the season. He played 13 times and scored 4 goals.
In January 2017, in the final hours of the January transfer window, Oxford United of League One announced that McAleny had joined on loan until the end of the 2016–17 season. Manager Michael Appleton was quoted as saying "He works hard, knows where the goal is and we think will give us another goal threat during the busiest part of the season." He scored his first goal for the club, the only goal of the game, in a 1–0 away League One victory over Charlton Athletic on 21 February, and followed up with a hat-trick in a 4–0 away win at Chesterfield the following Saturday. McAleny scored the second hat-trick of his spell at Oxford in a 5–1 home win over Bury on 28 March. He finished the season having scored 10 league goals in 14 starts.
On 23 June 2017 McAleny joined Fleetwood Town on a free transfer, signing a three-year contract. He scored twice for Fleetwood on his debut in a 2-0 win over Rotherham United on 5 August 2017.
McAleny represented Knowsley in the 2005 Merseyside Youth Games, participating in the 80-metre sprint, shot put and triple jump. He attended Knowsley Hey High School in Huyton.As of match played 30 April 2017.
Wigan Athletic: League One: 2015–16