Kilgetty-born Cullen joined the Swansea academy at the age of eight and made his senior debut in a 1-0 EFL Cup defeat by Crystal Palace under Graham Potter in August 2018.
He scored his first goal for the Swans in a dramatic 4-1 win over Reading on the final day of the protracted 2019-20 campaign, a result that saw Steve Cooper’s men secure a Championship play-off spot.
Cullen has scored 37 goals in 207 Swansea appearances across all competitions.
The Swans are hoping, though, to keep hold of last season’s Championship top scorer Zan Vipotnik and use former Celtic striker Adam Idah more consistently following his injury-hit debut campaign.
Cullen’s inability to be a regular starting number nine has often led the 27-year-old to feature in a deeper role, as he has done with Wales under Craig Bellamy.
Vitor Matos’ side have already added wingers Elijah Just and Moussa Yeo – who can also operate in an attacking midfield role – to their ranks this summer, in addition to Stephen Welsh, Joseph Opoku and Leo Walta.