Guinness-Walker was a rumoured target of the Robins but now they may have to move fast if they are serious in their pursuit of the player with other teams circling.
Championship rivals Huddersfield Town and Middlesbrough are also said to have looked at the player but the League One outfit look to be the front runners.
A report from The Sun claims that Pompey are ready to offer the Dons a fee for the player next month.
The Hampshire club have set aside a budget for the January transfer window as they plot a promotion push to the Championship.
The 22-year-old’s contract is up at the end of the season but rather than waiting until the summer, Portsmouth want to secure his services now as they regard him as one of the best in the division.
An academy product of both Chelsea and Tottenham Hotspur, Guinness-Walker left the two London clubs aged 11 and had an alternative route back into professional football. He played Sunday League and was signed up by the Metropolitan Police at 17-years-old.
After one full season with the club, he was signed up by the Dons and has gone on to play more than 80 times in the third level of English football.
Despite Danny Cowley’s side looking like the favourites to sign him, there is not a rush from City to rival a bid for the player at the moment, given there are enough options in that position.
The Robins operate mainly with a flat-back three with two supporting attacking wing-backs with Callum O’Dowda the preferred option at the moment.
Former Chelsea defender Jay Dasilva is also an option but he has fallen down the pecking order following the return to action from Cameron Pring.
Dasilva, who is reportedly on a considerable wage packet, could be moved on for a cheaper option in perhaps Guinness-Walker.
O’Dowda’s contract is also up at the end of the season so he could be a longer-term option but talks are expected to take place in January about which players’ stays should be prolonged at Ashton Gate.
There are alternative transfer options as well should City want to make a move in O’Dowda’s position. As well as links to Guinness-Walker, there has also been a suggestion about signing Swansea City left-back Jake Bidwell.
A report from the Swansea Independent says that both City and Birmingham City want to take Bidwell in the January transfer window.
The 28-year-old was wanted by Middlesbrough in the summer but a move failed to materialise and he has since gone on to play 16 times in the Championship in the current campaign.
It is understood however that the Welsh club are keen to keep him at the Liberty Stadium and that they begin contract negotiations with a player who is out of contract at the end of the season.