The 30-year-old is a free agent after his contract with Aston Villa expired at the end of the season and is on the lookout for a new club.
Pompey remain in administration, have no manager in place and are currently unable to sign players until a CVA is agreed, but are still drawing up a list of summer targets.
Harewood is one player reported to be in the sights of the Fratton Park outfit and would be willing to hold talks with the south coast club.
He failed to make an impact during his time at Villa Park but spent a brief and productive loan spell with Newcastle last term before a foot injury ended his stint in the North-East.
The powerful frontman has a solid goalscoring record from his time with Nottingham Forest and West Ham and agent Phil Sproson feels he will be one of the bargains of the summer.
Sproson said: "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.
"Portsmouth have still got some quality players there, so if they can keep the squad together I'm sure they could have a good season. Of course, players want to see stability and Marlon is no different.
"If Portsmouth are really keen to sign him and want to sit down with him to go through their plans for the future and can back it up, then he would be interested.
"If they want him to be a big part of it, Marlon would definitely listen."