According to a report in The Sun, Southampton were interested in moving for Gylfi Sigurdsson before he indicated that he wanted to stay at Swansea City.
Everton were the first Premier League side to lodge a bid for Sigurdsson this summer, with Ronald Koeman making him a top target.
However, the Saints were prepared to rival their former manager to bid for the Icelandic international.
Southampton have raised a sizeable amount of funds over the transfer window so far - through the sales of Victor Wanyama, Graziano Pelle and Sadio Mane - and they were prepared to reinvest some of those funds to sign the Iceland international.
Sigurdsson featured highly on the south coast club’s transfer wishlist, but he is set to reject all advances and stay at Swansea.
Sigurdsson was a key player for Swansea last season, and his performance at Euro 2016 also helped increase his reputation.
Sigurdsson's commitment to Swansea leaves both Southampton and Everton having to look elsewhere to find another attacking midfielder, with the Premier League season edging ever closer.