The U’s chairman this week revealed that a second offer from Bristol Rovers for the 28-year-old was rejected.
Thomas admitted he expects more interest – Northampton and Luton are rumoured to also be in the hunt – in Constable, who has topped the goalscoring charts at the Kassam Stadium for the past three seasons, over the summer.
United accepted an offer from Swindon in January for the striker, who is known as Beano, but the player turned down the chance to move.
The fact the U’s were prepared to allow Constable to talk to Swindon has alerted other clubs to the potential sale of the former Shrewsbury man.
But Thomas says the stance of United has never changed.
“We could have sold James very easily and we have said that consistently,” United’s chairman said.
“We wouldn’t have turned down offers if we wanted to get rid of James.”
Thomas does, however, accept that every player has his price, and that if an offer meets the club’s valuation, then there is the chance of a move.
“We are not the type of club that is going to turn round and say that none of our players are for sale,” Thomas said.
“Other clubs are in a position where they can turn down big offers for players, and we are not in that position. But we are also not in the position where we have to accept any offer that comes in for our players.
“If good enough money comes in for players, we will consider the offer.
“I’m sure clubs have seen we have accepted an offer and so it means it probably picks up their interest.
“I am very up front with the players and James knows the position the club is at.
“James has got two years left on his contract – we gave him a three-year deal last year – so I think that’s enough commitment from us to say that you are part of this club.”