The Uruguayan international has claimed that he is open to leaving Anfield due to the negative treatment he feels he has received from the British press.
"The last thing you want is an unhappy player and Liverpool know that," Molby 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."
Reports have claimed that the club are looking for a bid in the region of £40m for the striker.