It has been claimed Danny Cowley has made an approach for the forward and is set to take part in a bidding war along with unnamed League One clubs.
The 23-year-old fired in 30 goals in 35 National League South appearances for Wanderers last term, helping them gain promotion to the National League.
Rutherford penned a new two-and-a-half year deal to remain with the Surrey outfit in January after gaining interest from clubs higher up the football pyramid.
It was believed that Dorking placed a £200,000 valuation on him amid strong links elsewhere in the last transfer window.
Now it appears the striker is on Pompey’s radar, eight years after he was released by the Fratton Park outfit.
The Portsmouth-born forward came through the ranks at PO4, originally starting his career as a defender.
Despite being offered a two-year deal in 2014, the club withdrew their offer after the former Moneyfields ace was diagnosed with a heart condition called aortic stenosis during a routine medical.
After going against FA advice, Rutherford rejoined Moneys and would go on to have successful spells at Bognor and the Hawks.
Cowley has revealed he is keen to bring Portsmouth-born stars back to the south coast this summer, with Buckland boy Marlon Pack already returning to Fratton Park.
Pompey have also been reportedly linked with a move for Cambridge United striker Sam Smith.
The 24-year-old arrived at the Abbey Stadium on a free transfer last summer and netted 21 goals for the U’s in 57 outings in all competitions.
The forward enters his final year with Mark Bonner’s side after he penned a two-year deal in 2021.
Smith joins Rutherford on the ever growing list of names reportedly on Pompey’s radar as Cowley continues his desperate search for strikers.