The 30-year-old has already been approached by Panathinaikos, from Greece, and Turkish champions Bursaspor.
Currently on holiday in Barbados, he will leave a decision over his future for several weeks yet.
But agent Phil Sproson insists Harewood would welcome a Pompey approach.
And he believes the former Nottingham Forest man is definitely interested in kick-starting his career at Fratton.
Sproson told The News: "Getting Marlon on a free is going to be a fantastic deal for someone.
"He's proven, will get you 20 goals a season in the Championship and I am probably having an enquiry a week for him.
"It's a tad too early to decide where he will be next season. He wants to see what comes in.
"I do know he would be interested in Portsmouth and would welcome an enquiry.
"It's a big club and although its problems have been well documented, that wouldn't put him off. He can see what the club has to offer."