Speaking on Tuesday night after the FA Cup replay against Norwich, Meulensteen admitted that Fulham had had a bid for Morrison rejected by West Ham.
Meulensteen coached Morrison through Manchester United's youth systems during his time at Old Trafford.
"Yes, we did make a bid," Meulensteen said after the 3-0 win over Norwich. "Yes, I think he does want to come.
"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 our director Alistair Macintosh."
United academy product Morrison has impressed at Upton Park this season after a loan spell with Birmingham last term.
Morrison had struggled to settle in London after leaving Old Trafford in January 2012, but has hit form in this campaign.
Morrison is a real talent in spite of the 'off field' stories.I would be clearing out a lot of others in the squad before him including BFS.Love the 'dancing feet'- Roman0503