Saints will today try to salvage their move for Swedish striker Marcus Allback after their initial bid was turned down by Heerenveen.
Stuart Gray is thought to have offered around £2.5 million for the former Bari frontman who has a clause in his contract allowing him to leave for £2 million in May.
Saints hoped topping that figure would persuade the Dutch First Division side to cash in now.
But they are holding out for more than double the offer from Southampton who will not go much higher for a player who will soon be 29.
While Saints are prepared to pay their second highest ever fee, they will not smash their club record outlay for a player who would have little re-sale value by the end of a four or five-year contract.
Gray is playing his cards close to his chest saying only: "It has been well documented that is a position we are looking to strengthen but I am not going to comment on speculation."
However, Heerenveen president Riemer van der Velde confirmed: "Southampton have made a bid - but you can't really call it that. I do not think they are serious.
"We told them how much we wanted for Marcus and they told us what they are prepared to pay. The figures are a long way apart. I don't think they will be coming back."
Saints are unlikely to meet such an inflated asking price, thought to be around £5.6 million. But if Heerenveen drop their demands it will leave room for negotiation.
And Gray would be keen to re-open the deal for Allback who is a close friend of Southampton midfielder Anders Svensson.
The pair room together with the Swedish national side and talk regularly and Allback would be keen to link up with him at the Friends Provident St Mary's Stadium.
Allback said: "It is too early to talk about a transfer. If Heerenveen are asking £2.5 million, it sounds reasonable.
"I have a clause in my contract stating I am free to leave for around £2 million but only in May. In other months the club can put a higher price tag on me."
Meanwhile, Gray has dismissed reports linking him with Swedish midfielder Abgar Barsom of Djurgardens IF or with a £4 million bid for Chelsea midfielder Jody Morris.
He said: "There is no truth in either of those stories. Equally we have not heard from Tottenham who have been linked with Wayne Bridge. In any case he is not for sale."
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