The News understands it would take in the region of £300,000 to fund a move for the in-demand talent this summer.
And that is beyond what the Blues value the 22-year-old at, as Gills boss Neil Harris writes off the chances of retaining Tucker’s services.
A stack of clubs including the likes of Sheffield Wednesday, Ipswich Town, Hull City, Hibs and Scottish giants Rangers and Celtic have been linked with the 22-year-old.
Tucker first emerged on Danny Cowley’s radar last summer, with reports of a £200,000 bid being turned down for the man who came through the ranks at Priestfield.
A move never accelerated but the Pompey boss has followed Tucker’s progress since, as he made 50 appearances this season with his side relegated to League Two on the final day.
Tucker is out of contract this summer, but his next destination will have to pay Gillingham training compensation.
With the centre-half at the club since the age of seven, that bill is likely to run into hundreds of thousands.
Cowley is in the market for a new central defender, but it appears the total cost of the deal will be beyond what he’s willing to pay for Tucker.
Gills boss Harris confirmed a new contract is on the table for the man who’s made 137 appearances for his only senior club, but he expects Tucker to move on.
He told Gillingham’s official site: ‘Jack is ongoing (his position), I have been very clear and honest with everybody that he is likely to move on.
‘As much as I’d love to have him at the football club, realistically, we are not going to keep him even though we have made the contract offer.’
Meanwhile, Harris has also indicated he believes Ben Thompson will be operating at least in League One, as his Gillingham contract comes to a close.
Thompson spent a memorable six months on loan at Pompey in 2019, before being recalled by parent club Millwall in a dagger blow to the promotion hopes of Kenny Jackett’s side.
He has been regularly linked with a move to Fratton Park since, but Danny Cowley has opted against renewing his club’s interest to date.
Harris wants to retain the services of a player he knows well, but again knows that’s unlikely.
He added: ‘Thommo (Thompson) was on the retained list because legally we have to.
‘I spoke to him last week to see how he is getting on just in general.
‘Ben knows, as a football club, we are huge fans and we would love Ben Thompson to be at the football club.
‘But he is a good player, as we know, and have to accept that he might play at a better level than League Two next season.
‘While there is a chance, I will always be hopeful just because of the relationship I have with him, but it’s a real long shot and we’ll have to see what happens.’