Club captain Lloris, 36, wants a new challenge after over a decade at the club and is expected to leave this summer, despite having a year remaining on his contract.
Perisic, 34, also has 12 months on his deal and is attracting interest from a host of European clubs, having been persuaded to join Spurs last summer by former head coach Antonio Conte.
Both players are on significant contracts in north London and could seek compensation from Spurs to leave this summer.
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Hojbjerg is the target for several European clubs, including Atletico Madrid, and is also interested in a new challenge after three seasons in north London.
The Dane has two years remaining on his contract and Spurs will demand significantly more than the £15million they paid Southampton for the 27-year-old, although they are yet to receive any official proposals.
Spurs are also set to listen to offers for Davinson Sanchez, Joe Rodon, Ryan Sessegnon, Sergio Reguilon and Giovani Lo Celso but new head coach Ange Postecoglou is prepared to give players who want to stay a chance to impress.
Summer clear out: Hugo Lloris, Pierre-Emile Hojbjerg and Ivan Perisic could all leave Spurs
/ Getty ImagesAmong the Australian’s decisions is whether to give a lifeline to Tanguy Ndombele, who has struggled to make an impact in English football but is back at the club after another loan spell.
