Cleverley, who previously played under Martinez on loan at Wigan Athletic, is currently embroiled in a fight for Premier League survival as he nears the end of a temporary spell at Aston Villa.
Arsenal and Tottenham have both been linked with the 25-year-old, whose Old Trafford contract expires at the end of the season, but Martinez could be tempted to make his move when the clamour for the player begins.
"We know the situation with Tom," he said. "He's a player that I know well and have worked with him.
"At the moment he's fighting for something very important and is trying to achieve the aim for his club.
"Obviously that deserves respect. I wouldn't expect anybody to speak about my players and I would never do that [to anyone else]."
Martinez rubbished reports linking him with a move for Barcelona's Sergi Roberto, while no decision has yet been made regarding the futures of defenders Sylvain Distin and Antolin Alcaraz - both out of contract at the end of the season.
