An earlier report suggested that Southampton had received an approach from a Premier League club, but Hampshire Live claim the Saints are unlikely to sanction any sale.
Leeds were reportedly interested in offering the Saints around £10m for the Scottish forward, and were optimistic they could bring in the player who has scored three career goals against them.
However, Southampton are already short of attacking options and it looks as though Adams won’t be going anywhere right now.
Ralph Hassenhuttl has already lost Armando Broja and Shane Long from last season, leaving him with Adams, Adam Armstrong and new signing Sekou Mara.
Mara has only just turned 20, and has just over 1,000 minutes of senior football under his belt, while Armstrong managed just two goals in his first season at St. Mary’s.
Leeds unlikely to sign Adams
Jesse Marsch has been looking to bring in a centre forward all summer to compete with Patrick Bamford, Joe Gelhardt and Sam Greenwood.
Charles de Ketelaere was a name Leeds United were linked with for much of the window, but the Belgian decided to join AC Milan.
Efforts to bring in Rennes forward Martin Terrier have also been ramped up after the 25-year-old had a successful season in Ligue 1.
Bamford has returned to action in pre-season for Leeds after struggling for fitness throughout last season as Leeds secured Premier League survival on the final day.
The one-cap England international has shown that when fit, he’s good enough to lead the line in the Premier League, scoring 17 goals on Leeds’ return to the top flight.
However, that risk of the recurrence of the foot or hamstring injuries that hampered him last season mean Leeds need to either act in the market this month, or put a lot of faith in Gelhardt and Greenwood.