The club visit title holders Manchester City on the opening day of the campaign, while they have Manchester United at home and Arsenal away in their first four games.
With Wigan also visiting St Mary’s in that period, Le Tissier admits he would be delighted to see Saints come through that run with four points or more.
But he reckons Adkins will be aiming higher.
“If we were to get four or five points from those first four games I think most Saints fans would say that’s not a bad return,” said Le Tissier.
“But, obviously, Nigel will be a bit more positive than that. He’ll probably want eight or nine.
“In fact, knowing Nigel, he’s probably looking for 12.”
Despite the difficult beginning, Le Tissier believes there is plenty of reason for hope when assessing how the fixtures fall.
“It’s a tough start, but it gives us a chance at the back end,” he said.
“We’ve got quite a difficult December, January and February.
“But certainly the back end gives us a bit of hope.”
For all the debate about how tough the schedule is, Le Tissier is just pleased to see Saints back among the elite of English football.
“It’s brilliant,” he said. “I’m not going to complain much about the start, because it’s just nice to be back in that league again.”