The French stopper only joined Spurs in 2012, but he is already believed to have grown frustrated with life in north London.
A lack of Champions League football for a second successive campaign at White Hart Lane is thought to have tipped him over the edge, with this season having been a disappointing one for the Lilywhites.
Lloris has already confessed that a lack of top-level European action for 2014/15 may cause him to assess his options, and with that now a mathematical certainty he is expected to seek a transfer.
The 27-year-old is unlikely to be short of offers, with Monaco and Paris Saint-Germain both keen to lure him back to his homeland.
But Barcelona are thought to be front-runners, with the Catalan giants said to be looking to replace Victor Valdes.
Tottenham may also miss out on the top candidate to be their new manager to the Catalan club too.
Barca are believed to be lining up Frank de Boer to replace Tata Martino.