In the past three summers, the Scottish champions have banked around £35 million from the transfers of Victor Wanyama, Fraser Forster and Virgil van Dijk – all to Southampton.
But Celtic legend Dalglish insists there is likely to be far less interest from English Premier League clubs in Ronny Deila’s current squad.
“Celtic were sponsored by Southampton for a wee while there, weren’t they?” said Dalglish. “However, at the moment, I don’t see any current player – other than young Kieran Tierney – that Celtic can trade in for decent money and they’d be better off keeping him. Equally, the current group of players would be better off staying at Parkhead.
“I don’t believe that anyone in the Premier League would come in for them. One or two of the current side are on loan, so they’re not Celtic’s players anyway. Apart from Tierney, Tom Rogic has kicked on a bit and somebody might have a look at Nir Bitton but that’s about it.”
Left-back Tierney, who made his Scotland debut against Denmark last month, has already been linked with Southampton.
But Dalglish has no doubts the highly-rated 18-year-old will be best served by seeing out his contract with Celtic which runs until 2019.
“He doesn’t wear short trousers any more, so he can make his own mind up what he wants to do,” added Dalglish. “But just leave the boy to progress. Whatever course he is going to take, he will take.
“I don’t know enough about the situation and I wouldn’t like to presume that somebody is going to come in and try and whisk him away. He is playing for Celtic, he is Celtic’s player, he will be well contracted, it won’t be easy to get him out the door.
“He loves the club, he has supported the club, he has been everywhere with them so I don’t see too many plusses in him leaving right now.
“He looks very composed. There doesn’t look as if he’s got much in there that is going to rattle him. He has done particularly well. He made the two goals last weekend against Motherwell.
“He has come through the system at Celtic and I think it is important that the football club get local guys in because the punters want to relate to them.
“It is all very well and good being a Celtic supporter and going on the buses to the games, but he is not there because he did that, he is there because he can play. If you have got both, then I think it makes it special for whatever club you are playing for.
“The punters can relate to him much more easily than some of the foreign guys. But it doesn’t matter what your background is. If you can’t play, you can’t get a game. You have got to pick your best players and Tierney has proved he is one of Celtic’s better players.”