The former midfielder also says Liverpool is the best place for his development.
The young player was awarded with the club’s Young Player of the Year award at the club’s end of season awards show on Tuesday, but was booed by a small number of fans as he received the accolade.
That came after it emerged he is set to ask for a move away from Anfield, according to BBC Sport, after having failed to agree a new deal despite months of ongoing negotiations over a new deal.
Now, Souness says Liverpool fans would have every right to turn on him should he leave.
“Supporters would be entitled to turn on him,” he said.
“I mean they’ve shown great loyalty to him, the supporters support him through thick and thin and he’s turning his back on them. If he is, that would be very sad for the football club.”
The former midfielder does however want the youngster to stay at the club as he believes Liverpool is the best place for his continued development.
It is easy to forget that Sterling is still so young, having had an impressive rise in stature under manager Brendan Rodgers, with the increased game time at Anfield arguably having sped up his growth.
And Souness says he is far from the finished article, while the Liverpool supporters are the best he could play in front of as he learns his trade.
“He’s a young man with lots of potential [but] he’s far from being the finished article,” he added.
“He should stay at Liverpool, learn his trade and just get on with it. He’s at the best club he could possibly be at with the best crowd to play in front of. They’ll be patient with him; right now it’s all about him learning how to play the game.”