The Saints pair are rumoured to be close to leaving the club this summer on the back of impressive campaigns with the South Coast side, which have secured them both spots in England’s World Cup squad.
Shaw is reportedly on the verge of a massive £27m move to United as a part of Louis van Gaal’s first-team overhaul, while Lallana has emerged as a top target for Mauricio Pochettino following his switch from Southampton to Spurs.
The latter is also wanted by Liverpool, but an unsuccessful £20m offer – the Hampshire side want £25m – may well scupper a possible switch.
When asked by talkSPORT about the pair’s futures, Le Tissier said: “If those two decide to move on, with the talent they’ve got, they’ll move on to clubs that are already in the Champions League. Not sides that will have to challenge to be there next season.”
But Le Tissier went on to say that Shaw’s decision may be more complicated: “It’s a tricky one.
“Luke Shaw has been linked with Manchester United, who aren’t in the Champions League next season, but, with their history, it won’t be too long before they’re back in that top four.”