Ibrahimovic joined LA Galaxy in March this year after cancelling his contract with Manchester United and was expected to wind down his illustrious career in Major League Soccer.
However, a return of 20 goals in 24 games after a career-threatening injury has seen the veteran Swede linked backed to the San Siro.
Reports in Football Italia suggest Gatusso is keen to add further fire-power to his side and the former Rossoneri star would add valuable experience to his youthful squad.
However, the fiery Italian coach refused to be drawn into the furore surrounding the iconic striker, who recently joined Cristiano Ronaldo and Lionel Messi in the 500-goals club.
"Today is his birthday, so I wish him many happy returns," Gattuso said at a news conference ahead of Thursday's Europa League game against Olympiacos.
"I'll only speak about the players I have available. Ask Maldini, Leonardo and Scaroni.
"Today I just want to wish Ibra a happy birthday and wish him all the best.
"Ibra is 37 but he can still score goals."