Jordan joined Liverpool's academy at age six after being spotted playing for his school team. He made his U18-debut on his 15th birthday and came on as a late sub for Liverpool's U19s in a NextGen Series match against Inter Milan only ten months later. While the boyhood Evertonian was a regular for Liverpool's Under 21s during the 2013-14 season, the 2014-15 season saw him miss a substantial number of games due to injuries as well as regular involvement with the first team. In September 2014, the former Liverpool U16 skipper was named Liverpool's U19 captain for their UEFA Youth League campaign.
Having been named as a substitute for the first team twice during the 2013-14 season and made appearances in several pre-season friendlies over the following summer, Jordan made his competitive first-team debut in a League Cup fixture against Middlesbrough on 23 September 2014 and became Liverpool's second-youngest ever goalscorer as he netted the opening goal after ten minutes. He continued to be involved with the first-team squad on a regular basis during the 2014-15 campaign until a ruptured ankle ligament ended his season in late January. On 11 July, 2015, it was announced that he would join Liverpool's first team on their pre-season tour of Thailand, Australia and Malaysia. On 22 August 2015, Brendan Rodgers confirmed that Jordan was now considered part of the first-team dressing room and there were no plans to send him out on loan. Two days later, Jordan made his Premier League debut coming on as a 76th minute substitute to replace Lucas Leiva in a 0-0 draw at the Emirates.
Despite being best suited to a deep-lying playmaker roll, Jordan has been lauded as being "potentially a young Stevie G" by Liverpool legend Robbie Fowler.