Dempsey is currently undergoing medical tests with a view to rejoining Fulham on loan in January, while Meulensteen believes he has persuaded Berbatov to stay at Craven Cottage.
It would be a major double coup for the Dutch manager who has been in charge for just three matches and used to ply his trade at Manchester United as a first team coach under Sir Alex Ferguson.
Dempsey, 30, currently plays for Seattle Sounders following a disappointing season with Tottenham last year, but is available for January and February in the MLS close season.
Meulensteen, whose side lie second from bottom in the Premier League and face the daunting visit of Manchester City to Craven Cottage on Saturday, said: "He's (Dempsey)having a medical over the last couple of days and the next couple of days, so hopefully that will all work out.
"Clint has spent so many years playing in the Premier League.
"We know where his strengths lie whether it is coming in from the left or playing as a deeper striker or a number nine depending on who you are playing against.
"The most important thing is that he will be a good boost for us."
Dempsey, who is captain of the United States national team, played 184 league matches for Fulham between 2007-2012, scoring 50 goals, and while he was often looked upon as the club's talisman there were some fans who were not impressed when he decided to leave for Tottenham.
Meulensteen, however, believes the fans will give him a warm welcome.
"I'm sure they will," he said. "It speaks volumes for him that in his loan opportunity he wants to come back here."
While the arrival of Dempsey could be crucial to Fulham's progress in the new year it is the news that Berbatov, 32, could also stick around which is exciting for Fulham fans.
Berbatov's agent had insisted he was unhappy and wanted to leave in the last weeks of the Martin Jol era.
Meulensteen said: "That was before I took over. I had a chat with him.
"I know he is very committed to this club and the games we have in front of us.
"That's what we both said, concentrate on the games we have up to January and then review the situation as it comes."
Asked whether he believed he had persuaded Berbatov to stay, Meulensteen said: "I could well have done because look at the performances he has put in. He has been excellent, absolutely fantastic for us."
