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.