Liverpool turned down a £40m offer for the Spanish striker, 26, last week. And the Anfield club made it clear they would not welcome any further approaches for their World Cup-winning star.
But that will not deter Chelsea owner Roman Abramovich from stepping up the pursuit of his top target this summer.
A top Stamford Bridge source said: "It's true Liverpool have knocked back the first bid of £40m but it's highly unlikely that will be the end to it.
"Let's see what happens when an offer of £50m lands on Christian Purslow's desk."
Red Rom is now on holiday after spending two weeks at the World Cup finals in South Africa but will test Liverpool's resolve by upping his offer.
He is hoping a significantly improved offer will concentrate minds at a club that has failed to qualify for the Champions League. They are also £350m in debt and made a £55m loss in the last financial year.
Torres, who joined Liverpool for £21.5m from Atletico Madrid three years ago, met with new Liverpool boss Roy Hodgson and managing director Purslow this week in Spain. But that did little to stifle speculation surrounding his future.
And if the Kop favourite comes out publicly and demands to leave Merseyside, then Liverpool may reluctantly consider doing a deal. But sources close to the hitman, who will be out for three weeks after tearing an abductor muscle in the World Cup final, say he is in no rush to commit himself either way yet.
A Liverpool insider said: "The club were quick to reject Chelsea's £40m bid and tell them Torres is not for sale. "But the worry is it still won't be the end of it and that Chelsea will be back.
"Fernando could kill the deal stone dead by coming right out and committing himself to the club. Hopefully he'll do that sooner rather than later."
The Reds are closing in on a £12.5m move for Nice striker Loic Remy, who is regarded as one of the hottest prospects in France.
Remy, 23, said: "Liverpool are a legendary club. I'm very excited about the thought of playing there."
Roy Hodgson has reiterated that Liverpool have no intention of selling Fernando Torres after holding talks with the Spanish striker.
It is reported that Torres is considering his future at Liverpool following the club's failure to qualify for the Champions League and Chelsea are believed to retain an interest in the World Cup winner.
However, Liverpool are reluctant to lose any of their leading players this summer and Hodgson has firmly stated that as far as he and the club are concerned, Torres will not be leaving Anfield.
"I have met with Fernando. I found him to be a very pleasant man and we had a nice conversation," Hodgson told reporters.
"As far as we are concerned he is a Liverpool player and we want him to remain a Liverpool player. He is not for sale and we don't welcome any offers for him.
"We want to keep him. My conversation with him was only short because I had to leave to come to the training camp in Switzerland. We spoke about football, the World Cup, his injury, and I told him how much I am looking forward to working with him.
It is a similar situation for captain Steven Gerrard, who has been linked with a possible move to Jose Mourinho's Real Madrid over the summer.
"What we haven't had is a club wanting to buy Steven Gerrard. Steven Gerrard is not for sale - I made that clear to him. I told him I supported the club's policy that we don't want to sell our best players and have to start building again.''
Midfielder Javier Mascherano is also the subject of speculation and his agent has claimed the player is keen to reunite with Rafa Benitez at Inter Milan. Hodgson has tried to contact Mascherano to ascertain his future plans but says he has been unsuccessul so far.
"I have tried to contact Javier," Hodgson said. "I have left him voice messages and sent him texts but had no reply. To be fair to him, that's not unusual because he's had a tough World Cup and I believe he's gone back to Argentina.
"It's not always easy to get in touch with people. I have tried to reach him to make clear I am happy to talk with him at his convenience."
for 50 million pounds, Liverpool should throw in Kuyt as well...........