Kane is an instrumental figure in the Spurs frontline, having scored 24 goals in 30 appearances this season, but is set for an extended spell on the sidelines.
The 23-year-old has suffered ankle ligament damage and early fears suggested his season could be over but Mauricio Pochettino says the striker is now confident he can return ahead of schedule.
Sunday's clash against Claude Puel's side will definitely come too soon for the England international and Le Tissier believes Kane's absence could prove to be a leveller, particularly as Tottenham's other players could be knocked off their stride without their talisman on the pitch
"Their home form is absolutely outstanding so it's going to be a tough game," Le Tissier told Standard Sport.
"But - now Harry Kane is out it's a big blow. He's such a dominant force for them in terms of their goalscoring, as a leader and as a talisman.
"When such an important player in a team is missing it has an effect on the other players. They can look to him to get them out of trouble at times.
"If they do happen to go a goal down you look round the team and say 'right - where are we getting back into this?'"
While Spurs are still fighting for a Champions League place Southampton appear to have little left to play for this season following a controversial EFL Cup final defeat to Manchester United.
But Le Tissier is hopeful the prospect of fourth successive top-eight finish will be enough to motivate the South Coast outfit during the run-in.
And, as the last team to win a top-flight fixture at White Hart Lane back in May 2016, Le Tissier is convinced Puel's side will be aiming to record another upset this weekend.
"When that kind of player [Kane] is missing it does make a difference and hopefully we can take advantage.
"We had a good result there last year and so we have got nothing to fear even though they're a good team.
"They've got some dangerous players but the form we've been in the last few weeks we've got nothing to fear," Le Tissier added.
Matt Le Tissier is supporting Jeff Stelling’s latest unbelievable walking challenge for Prostate Cancer UK. Stelling aims to raise £500,000 on his March for Men. That’s 15 walking marathons in 15 days from June 2-16, from Exeter City to Newcastle United – St James Park to St James’ Park. For more details go to prostatecanceruk.org/jeffsmarch
The mega event is part of Prostate Cancer UK’s wider walking programme, March for Men, which includes a trio of Local Walks across Father’s Day weekend, including one in London on Saturday, June 17th. British dancer Wayne Sleep, is set to front the march and walk with his family and friends at the Queen Elizabeth Olympic Park, London. To find out more about the London walk go to marchformen.org