Meulensteen worked with the 20-year-old when they were both at Manchester United.
"We have put a bid in for Ravel Morrison but that got knocked back and we move on," Meulensteen told BT Sport after his side's 3-0 win over Norwich City in the FA Cup.
When pressed whether that meant the club had ended their interest in the attacking midfielder, Meulensteen refused to clarify Fulham's intentions.
"Yes I think he does want to come," he added.
"He would add pace, power, unpredictability and a real attacking threat. I don't know what the situation is now, because that's left with (club director) Alistair Macintosh."
Fulham and West Ham are both battling relegation from the Premier League.
The Cottagers are currently in 16th place on 19 points, just one point above the Hammers.