Cole arrived as a schoolboy at Manchester United, before coming through the academy. A notable game came in 2011, when he scored a hat-trick against rivals Manchester City in a 6–1 victory in the Premier Academy League. He then went on to make an impact in the club's run to the FA Youth Cup final, scoring a penalty and setting up teammate Ravel Morrison on the way to a 3–2 comeback against Liverpool in the quarter-final. Cole made his only senior appearance for Manchester United in the League Cup on 20 September 2011, coming as a substitute for Federico Macheda in the 77th minute of a 3–0 third round victory over rivals Leeds United at Elland Road. On 14 May 2013, Cole scored a hat-trick, including two penalties, against rivals Liverpool in the semi-final of the Under-21 Premier League as Manchester United won 3–0. Six days later, he scored two goals against Tottenham Hotspur in the Under-21 final at Old Trafford, as Manchester United won 3–2.
Fulham
On 31 January 2014, Cole joined fellow Premier League team Fulham for an undisclosed fee, along with Manchester United teammate Ryan Tunnicliffe, joining up with former Manchester United coach René Meulensteen. He made his debut on 9 February in a 2–2 draw against his former club at Old Trafford, coming on as an 80th-minute substitute for William Kvist. Following Meulensteen's sacking as Fulham manager, Cole and Tunnicliffe were deemed surplus to requirements by Meulensteen's replacement, Felix Magath. On 25 February 2014, Cole joined League One side Milton Keynes Dons on loan until the end of the 2013–14 season. He made three appearances for the Dons, while his parent club ended the season with relegation to the Championship. Cole did not play a single competitive game in 2014–15. On 1 September 2015, the last day of the 2015 summer transfer window, Cole returned to League One, with promoted club Shrewsbury Town, on loan until January 2016. He made his debut four days later, replacing the injured James Wesolowski in the 16th minute of an eventual 2–1 win at Barnsley for the team's first league win of the season. He then provided two assists for Jean-Louis Akpa Akpro in a 2–0 victory over Blackpool on 26 September for Shrewsbury's first home win of the season. His first senior goal came in a 3–1 defeat to Walsall at the New Meadow on 1 December. He later extended his loan deal until the end of the season, making a total of 34 appearances in all competitions, scoring 3 goals. On 31 August 2016, Cole signed for Scottish Premiership club Inverness Caledonian Thistle on a loan deal until January 2017. He scored his first goal for the club in a 1–1 draw with Hamilton Academical on 10 December 2016. In January 2017, the loan deal was extended until the end of the 2016–17 season.
Tranmere Rovers
On 27 October 2017, Cole signed for National League club Tranmere Rovers on a deal until January 2018. Cole made his Tranmere debut the very next day, coming on as a substitute and scoring in a 4–2 home win against Halifax Town. Four weeks later, Cole doubled his Rovers goals tally, scoring the opening goal in a 2–2 draw away to Macclesfield Town on 21 November. Cole extended his contract with Tranmere at the end of the 2017–18 season, but after just over a year with the club, he was released in January 2019.
Cole was called up for the England under-19 friendly against the Netherlands in August 2011 and went on to make his debut as a substitute in the 0–0 draw on 1 September 2011. On 28 May 2013, he was named in manager Peter Taylor's 21-man squad for the 2013 FIFA U-20 World Cup. He made his debut on 16 June, in a 3–0 win in a warm-up game against Uruguay.