According to Edinburgh Live Sport, Hearts – one of four clubs apparently monitoring the 24-year-old’s situation – are not interested in the player, with manager Robbie Neilson focusing his transfer attentions elsewhere.
And that leaves the Blues Lincoln and MK Dons battling it out for the attack-minded ace’s signature.
A report from the East Anglian Daily Times claims Michael Appleton’s Imps are leading the race for Bishop, who has been told by Tractor Boys boss Paul Cook that he can leave the club.
But it has also been suggested that Pompey could jump to the head of the queue if a swap involving fellow attacking-midfielder Michael Jacobs could be worked out.
The News revealed last month that former Wigan ace Jacobs had been given permission to speak to Ipswich, with the 29-year-old a pivotal player under Cook during the Latics’ League One title win in 2017-18.
However, he will not be allowed to leave Fratton Park unless it is on the Blues’ terms, with Cowley a big admirer of Jacobs, regardless of his injury record during his time at PO4.
Despite Pompey’s League One rivals tiggering a clause in Bishop’s contract at the end of last season, he is currently training with the under-23s at Portman Road alongside Kayden Jackson, Myles Kenlock and Flynn Downes.
All four are expected to leave the promotion hopefuls this summer as Cook carries out a major overhaul of his playing squad – a rebuild that has already seen 20 senior players depart.
Bishop has played 132 times for the Tractor Boys since making his debut in 2014.
Last season he made 38 appearances, scoring four goals.