With the transfer window shut to Premier League clubs, but open for those in the Championship and below to make loan moves, QPR boss Harry Redknapp has claimed his side are aiming to tie up a deal for the former Manchester United man.
And if Redknapp's promotion candidates can secure a return to the top-flight, they would surely become favourites to get Morrison on a permanent basis if West Ham were to let him go, particularly given the relationship between the east London club and Fulham following events last month.
Fulham had a transfer bid for Morrison rejected in January, with the Hammers accusing the Cottagers of an illegal approach.
Meulensteen insisted Morrison wanted to join Fulham when speaking after his side's 3-0 FA Cup replay victory over Norwich on January 15, sparking West Ham's grievance.
Now Meulensteen can only watch on from the sidelines.
"There's not very much we can do at this time, and what other clubs do we can't affect," said Meulensteen.
"The only thing I can affect is what we're doing at Fulham."
Fulham host Liverpool in Barclays Premier League action on Wednesday night, the game going ahead unaffected after planned London Underground strikes were called off at the last minute.
Buoyed by Sunday's 2-2 draw at Manchester United, Meulensteen admitted subduing Luis Suarez and Daniel Sturridge could be the ultimate challenge.
Meulensteen believes Liverpool boss Brendan Rodgers deserves high praise for winning the fight to retain Suarez and reintegrating the Uruguay goal machine seamlessly after his ban for biting Chelsea's Branislav Ivanovic.
"It's been a job very well done from Brendan Rodgers to keep him at Liverpool and help him have the season he has had," said Meulensteen.
"How do you stop them? They've had an incredible season, the pace and the penetration, the variety and the unpredictability in the way they can all score goals.
"So it has to be all hands on deck for us to make sure that we defend in a good, compact manner, that we keep communicating, don't leave gaps for them to get through and play through.
"But the defensive performance from Sunday was definitely a massive improvement, and we can build on that."
Former Manchester United manager Sir Alex Ferguson questioned Liverpool stalwart Steven Gerrard's status as a modern great in his recent autobiography.
Meulensteen worked at Ferguson's side for scores of United-Liverpool grudge matches, and rates Gerrard as among the best the Premier League has to offer.
"In my opinion he is a top player, definitely," said Meulensteen.
"Brendan [Rodgers] is looking at the players available and where he will best slot in as well.
"If Lucas would be fit, then probably Lucas would play a bit deeper and Gerrard a bit freer.
"But he probably thinks Gerrard is the best to play the deeper role now, it suits him, he's got the range of passing to do it, so he's still a very important player for Liverpool."
Kostas Mitroglu's knee injury continues to keep Fulham's new recruit sidelined, while defender Fernando Amorebieta will also miss out, but should return to training this week.
Hailing the impact of Everton capture Johnny Heitinga, Meulensteen said squad stalwarts Brede Hangeland and Scott Parker will fully understand being overlooked for the starting XI in Sunday's Manchester United clash.
"Johnny's been brilliant," said Meulensteen.
"He's an established Dutch international, has vast experience and best of all he's a leader, he talks.
"Both Scotty and Brede are top, top players, and every manager would want players like that in their squad.
"That's why they've been around for many, many years.
"They are the first players to understand when a manager makes those sorts of changes, which they would not necessarily be happy about, but will accept and do everything they can if and when called upon."