The Celtic midfielder has not been able to agree personal terms with the Saints even though the south coast club had a bid accepted for the Kenya international
Victor Wanyama has rejected an approach from Southampton after Celtic accepted a bid for the highly-rated 21-year-old midfielder.
On Saturday Goal reported that Liverpool, Everton and Cardiff had also joined the hunt for Wanyama, though Southampton had hoped to steal a march on their rivals with a £12 million bid accepted.
But the Kenya international could not come to an agreement with the Saints, although he insists he is still open to offers this summer.
"While the bid was okay for Celtic, the terms were not right for myself and my agent," Wanyama told the Southern Daily Echo.
"I am open to what offers are made, but I am relaxed and it's important that Celtic are happy too."
Wanyama made 49 appearances for Celtic last season.