Southampton are still fighting to sign Toby Alderweireld despite the Atletico Madrid defender having a medical at Tottenham.
It is understood the Belgium international has completed a medical and agreed personal terms at Spurs after their chairman Daniel Levy spent the weekend in Madrid agreeing a deal to bring him to White Hart Lane.
But Sky sources say Southampton, who believe Atletico are obliged to sell them the player, have now submitted a renewed bid of £14.2m.
That is more than double the original £6.8m figure written into last season's loan agreement to make the move permanent, and more than Spurs' agreement with Atletico.
And Southampton claim Atletico have overshot the time-frame set out to buy Alderweireld back out of their agreement, which they could have done at a cost of £1.5m.
Sky Sports reported last week that Spurs had made Alderweireld one of their top targets this summer and were determined to make him a Tottenham player as Mauricio Pochettino bolsters last season's leaky defence.
Alderweireld played 26 times last season as as Southampton conceded 20 fewer Premier League goals than Spurs.
He moved to Madrid from Ajax, where he also played with Jan Vertonghen and Tottenham forward Christian Eriksen, in 2013, but only started 10 times as Atletico won La Liga in 2013/14.
Born in Antwerp, Alderweireld was an Ajax academy graduate who played over 100 games for the club and won the Eredivisie three times between 2011 to 2013. He has 47 caps for Belgium.