The 31-year-old is due to return to Albion following a season-long loan from The Hawthorns, although the Whites do have an option to keep him at Craven Cottage.
And the former Manchester United midfielder has given the green light to stay in SW6 - if he's wanted.
He told the Fulham and Hammersmith Chronicle: "I've really enjoyed this season at Fulham, and it's up to the manager and the club now to sort out if they want me to stay.
"I'm really happy here, it's been a great year. To finish 12th in the best league in the world and reach the Europa League final has been brilliant."
Greening made just 15 starts in the Premier League for Fulham last season, but did feature heavily in their run to the Europa League final.
He admits he would have more chance of regular first-team football in the Midlands, but would rather battle it out with Danny Murphy and Dickson Etuhu for a slot in the Whites engine room.
"At West Brom I was playing every game," he added.
"You get used to playing week in, week out and when you haven't played for three or four weeks it's hard to come back in and play as well as you usually can do.
"It's an option to go back there as I have a year left on my contract, but I want to stay at Fulham. We said we'll speak after the Europa League final."