Veteran midfielder Parker was rested for Saturday’s win at Blackpool after picking up a slight knock against Rotherham in midweek.
With Fulham’s safety finally assured boss Kit Symons could make changes, with the likes of Cauley Woodrow, Shaun Hutchinson, Jack Grimmer and Seko Fofana in contention for recalls.
Midfielders Lasse Vigen Christensen (hamstring), Emerson Hyndman (collarbone) and George Williams (knee) are set to miss out again.
Middlesbrough head coach Aitor Karanka will make a late check on leading scorer Patrick Bamford after the 19-goal striker damaged an ankle in last Friday’s hard-fought win at Norwich.
Midfielder Albert Adomah is in a similar position after also hurting an ankle at Carrow Road, and he too will be assessed before Karanka names his team.
However, striker Jelle Vossen is more of a doubt after sustaining a series of knocks, the most troubling to his ankle, and he faces a race against time if he is to make it, while Jonathan Woodgate is struggling to overcome a hamstring problem.
Boro will be without Woodgate’s fellow central defender Tomas Kalas following his return to Chelsea after his loan deal expired, while Damia Abella (knee) and Rhys Williams (Achilles) remain on the sidelines.