West Ham reported their London rivals to the Premier League following comments from Meulensteen after his side's FA Cup replay win over Norwich on Tuesday, where he revealed a bid had been made and claimed Morrison wanted to move to Craven Cottage.
The Dutchman was understandably cautious to say any more on the matter at his press conference on Thursday afternoon.
When asked about any targets the club might have, he said: "I am not going to make any comments on (transfers) because it is going to get me into trouble.
"It is wiser at this moment in time that we are not going to comment on anything that is happening in regards to any transfer news or speculation.
"Things are in hand with the club, with (chief executive) Alistair Mackintosh."
With Morrison's contract at West Ham still having 18 months remaining, the east London club's complaint is likely to surround Premier League rulings which relate to a club making an approach for a player under contract or the player, or his representative, approaching clubs in the hope of instigating a possible transfer.
Asked if there had been any formal communication from the Premier League, Fulham's communications director Brookes stated: "We have only seen what you have seen. Up until anything further can be said, we will be making no further comment."
Morrison, meanwhile, seemed to refute recent suggestions he wants to leave West Ham.
Having earlier tweeted to suggest reports surrounding his future, including some which hinted that he may go on strike to push through a move, were "lies", he told the club's official website: "Although it is frustrating to read some of the reports in the media, I always try to keep my focus on the next game and show people with my performances on the pitch that I want to do well for West Ham.
"I've been working really hard over the past few weeks to get back to full fitness after missing a couple of recent games with a groin injury.
"I'm feeling fine now and I'm hoping to be involved in Saturday's important game with Newcastle and then the Capital One Cup semi-final with Manchester City on Tuesday."
West Ham assistant manager Neil McDonald took the Hammers' press conference on Thursday, standing in for manager Sam Allardyce, who was said to be busy with transfer business of his own.
McDonald stressed Morrison was happy at Upton Park and claimed reports the player threatened to go on strike to force a move were "news to (him)".
When asked if the club wanted to keep the 20-year-old, McDonald replied: "Well why not? But he needs to get into the team and he needs to be consistent. I imagine every player has a price."
Fulham are fighting for Premier League survival, having been thumped 4-1 at home by fellow strugglers Sunderland last weekend, and could do with some reinforcements.
Meulensteen accepts in general the mid-season transfer window can be "unsettling".
"It is always the financially strong teams who have the ability to strengthen, whether it is a push for the title or to get themselves out of the mess, whereas the teams who have not got that, you just have to deal with that," he said.
"But (the January transfer window) is definitely unsettling in many ways because of what clubs do, this that and the other, players get a bit unsettled with what is happening and what is not happening."