The Uruguayan striker scored 30 times for the Reds last season but admitted in May he had become unsettled in England, where he has often been criticised by both the press and Football Association for controversies with Patrice Evra and Branislav Ivanovic.
It is the 10-game ban given to him by the FA for biting Ivanovic that appears to have precipitated the 26-year-old's desire to leave, with moves to both Bayern Munich and Real Madrid mooted.
|33/1||Liverpool are 33/1 with Bet365 to win the Premier League this season
"The last thing you want is an unhappy player and Liverpool know that," the Dane, who played nearly 300 times for the club in a 12-year career at Anfield, told BBC Radio Merseyside.
"They've been busy in the market and it appears they're almost readying themselves for life without Suarez.
"I think he's made it pretty clear that he would like to try something new, including playing at a club that's in the Champions League. If that's how he feels, the club has to do the business."
Molby also believes Pepe Reina may join Suarez in moving on, particularly after Liverpool spent £9 million on Sunderland's Simon Mignolet.
"I'd be surprised if both of them [Suarez and Reina] were here on 1 September," he continued.
"Could you imagine Mignolet wanting to come to Liverpool and not play? He has his own ambitions and one of them is to be part of a very exciting Belgian national team.
"The fact we've signed another goalkeeper now - is it to increase competition for places? I don't know.
"In the first three or four years Pepe was here, he was as good as the club's ever had and as good as there was anywhere in the world.
"He hasn't quite been the same in the last couple of years, but I think he's a great goalkeeper. Possibly the time has come for him to move on, and if there's an opportunity for him back in Spain, so be it."