The 21-year-old England international has spoken to Aviva Premiership side Bath and Sale are also reported to be interested in acquiring his services.
Saints hope to agree new terms with the player, who is contracted until the end of the 2011 Super League season, but are thought to have made their final offer.
Talking on Saturday night, Eastmond said: “It will definitely be sorted this week – 100 per cent.
“Obviously I’m contracted here until the end of the season and I love St Helens – I am going to do my best to win games and trophies for Saints.
“But one way or another it will be sorted and that’s all I want to say about it.”
Eastmond hails from Oldham but joined Saints at the age of 13 and came through their youth system before breaking into the first team in June 2007.
He scored in the 2009 Grand Final loss to Leeds but missed last season’s Old Trafford showpiece through injury.
He returned to the side for Saturday’s dramatic season-opening draw against champions Wigan at the Millennium Magic event in Cardiff.
Saints had trailed 16-0 to their rivals before hitting back with late tries from Jon Wilkin, Tony Puletua and Francis Meli.
Eastmond had a chance to win the game but his last-gasp drop-goal attempt drifted just wide of the upright.
“I thought I’d got it but obviously not,” said Eastmond. “But it’s not about me, as a team we came back from three tries down to get a draw and that is the most important thing.
“It was a bit rusty from both teams but we will get on with it now. We were as scrappy as any team that’s going out there over the two days.
“But there was no way we were going to give up. At 16-0 if you score one try you are back in it and that is the way we look at it all the time.
“We were unlucky – although they could probably say they were too because they nearly scored another try.”
Wigan coach Michael Maguire was content to share the spoils and admitted his side’s first-half defensive heroics took their toll as Saints fought back.
“It’s credit to St Helens to be able to come back into the game,” he said. “When you’ve got the ball, you’ve got to hang on to it.
“In the second half St Helens did that. Unfortunately, we let ourselves down in a number of areas in our defence which we are normally very sharp at.
“In the first half we were outstanding with our scrambled defence close to our line.
It was a great effort from our boys. It’s good to get away with one point.
“There are things we can definitely work on between now and the next game.
“We will get a lot out of this opening game of the season.”
St Helens will anxiously await the news on Paul Wellens, who has been struggling with a rib injury from the end of last season.
“We’ll just have to monitor it,” said coach Royce Simmons. “Touch wood it’s not a recurrence because he might have to have minor operation if is.”
St Helens: Wellens, Gardner, Shenton, Lomax, Meli, Wheeler, Eastmond, Graham, Roby, McCarthy-Scarsbrook, Soliola, Wilkin, Moore. Replacements: Puletua, Clough, Foster, Dixon.
Wigan: S. Tomkins, Goulding, Gleeson, Carmont, Charnley, Deacon, Leuluai, Lima, McIlorum, Coley, Hoffman, J. Tomkins, O’Loughlin. Replacements: Hansen, Prescott, Mossop, Farrell.
Referee: Richard Silverwood (Dewsbury).