The Dutch international has been a shining light in what has been an otherwise poor season for the Cottagers, netting four goals in 13 league games after arriving from Besiktas in January.
The 32-year-old only penned a six-month deal at Craven Cottage and has already suggested he may move on with Fulham returning to the Championship.
And Parker revealed in his press conference on Thursday that he will have no issue with Babel if he opts to leave.
He said, "I totally understand Ryan Babel and he is probably in a similar position to what I was in at West Ham.
"He's been fantastic for us and Ryan stated it himself that his next move will depend on the offers he gets.
"I understand his position and situation, and it's not something that I want to hold him back from in any way.
"At the same time, Ryan is a player who we like a lot and he's been a massive part of what we've been doing."