Born in Liverpool, Jennings played youth football at Liverpool before being released as schoolboy. He soon joined Tranmere Rovers in 2008, having played for other clubs and having visited Rovers for a trial. He made his club and Football League debut on 18 September 2010 in Tranmere's 1–1 draw against Charlton Athletic, coming on as a second-half substitute. On 28 September 2010, he scored his first goal for the club in a 1–0 win against Bristol Rovers in his third senior match for the club. On 20 October 2010, Jennings signed his first professional contract, which would run until the end of the 2011–12 season. 10 days later, he scored a brace and made two assists in the 4–2 victory over Milton Keynes Dons. On 13 November, Jennings scored a winner against Plymouth Argyle with a twisting run from the halfway line. In October 2010, Jennings received the award for Apprentice of the month from the LFE. His goal against Plymouth helped attract interest from larger clubs, and Tranmere rejected an offer for Jennings from an unnamed Premier League club in the 2011 January transfer window. In March 2011, he was voted League One Apprentice of the Year at the Football League awards and in May 2011 he was announced as Tranmere Rovers' Young Player of the Year.
Bayern Munich
In July 2011 Jennings was signed by German club Bayern Munich, where he would initially play for Bayern Munich II the reserve team in the Regionalliga Süd. In late October 2011, Jennings' habituation into Germany was hindered after he suffered multiple ligament tears in his knee, sidelining him until March 2012. On 11 October 2012, Jennings scored his first goal in a Bayern shirt in a 2–0 friendly win over SpVgg Unterhaching. On 27 October 2012, Jennings scored his first competitive goal in Germany in a 2–1 loss away at Würzburger Kickers, with his second following just six days later in a 2–2 draw at FC Augsburg II.
Barnsley
On 18 June 2013, it was confirmed Jennings had signed for Barnsley on a three-year deal for a fee of £250,000 from Bayern Munich. Upon arriving, Jennings spoke of disappointment of having not broken into the first team squad at Bayern Munich and his excitement at Barnsley and his eagerness to do well there. On 3 August 2013, he made his Barnsley debut against Wigan Athletic, coming on as a substitute in the second half for Tom Kennedy; however, he was sent off just five minutes after he came on, having misjudged a challenge on Wigan's James McArthur. Subsequently, he was suspended for the following three games. While suspended, Jennings scored a hat-trick for the reserves and he scored his first senior goal for the club on 8 March 2014 in a 1–0 win against Nottingham Forest.
Milton Keynes Dons
On 30 June 2015, following his release by Barnsley, Jennings signed for Championship side Milton Keynes Dons on a one-year contract having previous played for the club on loan for a short period in 2013. On 1 February 2016, Jennings left the club following the mutual termination of his contract having made only two appearances since signing.
Return to football
On 28 September 2018, Jennings signed for non-league club Runcorn Town looking to "resurrect his career", with a view to returning to playing in the Football League once again. He made his debut for the club on 3 October against Congleton Town and three days later he scored his first goal for Runcorn in a 3–0 away win against Silsden.
Personal life
In August 2017, Jennings' eldest daughter was diagnosed with leukaemia.
