The France international, who swapped Camp Nou for the Stade Louis II last year, wants the out-of-contract goalkeeper to follow him to Monte Carlo.
The Spain international is out of contract at the end of the season and has already stated he will not be signing an extension.
Consequently, Abidal, who made the move from Camp Nou to the Stade Louis II last year, is hoping that Valdes follows him to Monte Carlo.
"If Valdes has the dream to come and play in Monaco, I will welcome him with open arms," the defender told Cadena SER. "I have a room for him in my house, and I will help him find a house near me!"
Abidal also insists that he holds no ill will toward Barcelona, even though he wanted to extend his stay in Catalunya.
"I'm very happy in Monaco," he said. "There are a lot of good people here, and I'm playing every game. I only ever wanted to play football. But I have no problems with [Barca president] Sandro Rosell or [sporting director] Andoni Zubizarreta. My contract expired and I fought to renew it, but it wasn't to be.
"But Barca have already told me that the door remains open for me to become director general of their football schools."
Abidal, who underwent a liver transplant in 2012, also revealed that his thoughts are currently with former Barcelona boss Tito Vilanova and his ongoing battle with cancer.
"I pray for him every day," the 34-year-old said. "He is a fighter, and hopefully he'll come out of this.
"I have pills that I have to take for the rest of my life. Life is complicated, but you have to enjoy it to the fullest."
Abidal also had his say on the battle for the Ballon d'Or, which he hopes will be awarded to France teammate Franck Ribery over Cristiano Ronaldo and Lionel Messi.
"He's a very good friend and has had a great year," the center half stated. "It would be good for French football as nobody has won it since [Zinedine] Zidane [in 1998].
"But both Messi and Cristiano have incredible numbers that would also be worthy of the award."