Fulham bid rejected for Morrison
But the Cottagers boss claims he believes the former Manchester United youngster is keen on a move across the capital.
Meulensteen coached Morrison through United's youth systems, and is confident he has a chance of linking up with the 20-year-old again.
The Dutch coach is likely to discuss the situation with Fulham director Alistair Macintosh in the coming days.
"Yes, we did make a bid," Meulensteen said after Fulham's 3-0 FA Cup third round replay victory over Norwich at Craven Cottage.
"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 Alistair Macintosh."
United academy product Morrison has impressed 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.
And that has alerted a host of clubs keen to prise him away from Upton Park this month.
Cardiff are rumored to be prepared to fight for the England Under-21 international's services, and Meulensteen said it is still too early to tell whether any deal can be struck between Fulham and West Ham.
"We got knocked back, it got rejected, and so we need to review it and move on.
"I've explained how I think about the situation (to the Fulham board), so we'll have to wait and see what happens.
"I've known him for a long, long time, but the thing is this: we have to wait and see how the club takes it forward as to whether there's another bid."
Expecting Morrison's situation to run until the wire, Meulensteen admitted he still harbors personal hopes a deal can be struck.
"Well that's what we're hoping for," he said.
"I've made my desires clear so I'll leave it up to the relevant people to take forward. I don't know the ins and outs. It's very difficult in the January transfer window.
"People always say, 'Why don't you do your business early', and the answer's simple, because you can't.
"Clubs are in a similar situation, they know the longer they wait the higher the price will go. Or they gamble and nothing comes off.
"So you always see things stretching to the last week of the transfer window."
Fulham's head coach also confirmed Costa Rica striker Bryan Ruiz has completed his loan move to PSV Eindhoven, with the Dutch club set to confirm the deal on Wednesday.
Meulensteen said: "Yes, I think he's signed and that should be announced tomorrow (Wednesday) morning.
"That's a loan deal until the end of the season."