France's national soccer team captain Hugo Lloris
The Frenchman, 29, has been a key part of the Spurs side ever since his 2012 move from Lyon, and was a major factor in Tottenham's superb defensive record this past season.
Stoke's Jack Butland
However, The Mirror now report that Lloris - set to captain France at this summer's European Championships - has snubbed the offer of a new five-year deal at White Hart Lane.
Spurs don't appear to be in any huge rush to sell Lloris, and the report adds that chairman Daniel Levy remains confident of securing a new deal with the goalkeeper, who is believed to be looking for a little more money before penning a new deal.
Tottenham's Hugo Lloris before the game
After the reports broke, Spurs fans took to Twitter to suggest that, whilst Lloris is a key player under Mauricio Pochettino, it may not be the end of the world for the club if he does leave at some stage in the near future.
Lloris' form dipped towards the end of the season as Spurs' title bid fell apart, and fans claimed that if Lloris does go, it should be Stoke City star Jack Butland brought in to replace him.
England's Jack Butland during the national anthem before the game
The England international has impressed with Stoke City, and given that he is just 23, Butland would add to the growing base of young English talent at White Hart Lane.
Jordan Pickford of Sunderland also received an honourable mention, but Butland was a popular target amongst fans - even though there is still a high chance that Lloris, who is contracted until 2019, will stay at White Hart Lane for some time yet.
Here are some of the reactions after Lloris allegedly rejected a new deal at White Hart Lane...
<whispers> I would be okay if we for some reason sold Hugo this summer*— Shaun Ranft (@Shaun_TSP) June 1, 2016
*but you better damn well have a very good backup plan. #THFC
Now what exactly is Monsieur Lloris up to? Didn’t have a very good end of season. #THFC— Stuart Peel (@JedLomax) June 1, 2016
Lloris was slightly above average at best last season IMO. Not that I think we should be looking this summer #THFC— Andrew Labib (@Andrew_Labib) June 1, 2016
Can see Hugo leaving if he doesn't want sign the new contract #thfc— D_Spurs (@Dan_Jax) June 1, 2016
Doubt Hugo rumours are true but if he does go we'll easily get £25-30M for him. Buy Butland & Pickford, we'll survive. #THFC— Hotspur F.C (@HotspurFC82) June 1, 2016
Love Hugo and would rather him stay for continuity purposes but if he goes I think Butland would grow into a more than capable replacement— Lee Sadler (@Sads3110) June 1, 2016
IF Hugo has rejected a deal, it's not the end of the world, I think there's options out there for us to sign a keeper. I'd fancy Butland.— JC (@Jack_Webster4) June 1, 2016
Would you sell Lloris and sign Butland?