Jose Mourinho claimed on Wednesday that the 27-year-old was the only transfer target that the Blues were interested in this summer after placing a bid 24 hours earlier.
"The PFA would be happy to support any player in whatever situation they're going through," Carlisle is quoted as saying by Goal.com. "If they feel that they need our advice and our support we are there 24/7 for every player across the game.
"In a situation like this that's beyond our jurisdiction, we have no control over the press and what they say, we have no control over supporters and what they say.
"All we can try and ensure is that Wayne Rooney has the support that he needs and that in any dealings that go on they follow due process."
Rooney arrived at Old Trafford from Everton in 2004 for around £25m.