But goalkeeper Pepe Reina looks to be on his way out, with Serie A side Napoli heavily linked to the Spaniard.
Suarez, 26, missed the first leg of the club's Asia tour in Jakarta after being given time off by the Reds following the Confederations Cup, but he flew into Melbourne from Montevideo late Sunday.
He has made clear he is keen to move to a club playing Champions League football, and has been the subject of a rejected £30 million bid from Arsenal.
But pressed on whether he expected Suarez to remain at Liverpool for the upcoming season, Rodgers told a press conference: "Yes, very much so."
"There's been a lot of speculation over the course of the close season but the reality is that he's a player who is very much valued at Liverpool and unless there's any sort of offer that comes in that's anywhere near his value, there's nothing to consider," he said, adding: "We haven't had that."
The Gunners are believed to be considering returning with an improved offer, while Chelsea and Real Madrid are also said to be interested in the controversial former Ajax star, who will miss the start of the Premier League season while he completes a suspension for biting Chelsea's Branislav Ivanovic.
Asked what Suarez's value was, Rodgers replied: "I didn't say we would sell him. I said that every player has a value and a worth. Doesn't mean you've got to sell them."
Rodgers, whose side beat an Indonesia XI 2-0 in Jakarta on Saturday, plans to sit down with the striker in a bid to persuade him to stay.
"We'll chat at some stage, like I do with all the players," the manager said.
"But he's back, he's in great spirits. He's obviously an integral part of the group -- you could see his closeness with his teammates last night when they were all seeing him for the first time in a number of weeks.
"He'll join training today with all the other players and over the course of the next few weeks we'll communicate."
With Suarez yet to start training, it seems unlikely he will figure prominently in Wednesday's sell-out friendly against Melbourne Victory at the Melbourne Cricket Ground, although Rodgers suggested he could play a part.
"They will all be involved, they will all have some part to play," said the manager.
One player who does appear to be on his way out of Anfield is Reina.
The Spaniard has been linked with a move to Napoli, now managed by former Reds' boss Rafael Benitez, following the arrival at Anfield of Simon Mignolet from Sunderland.
Asked for an update, Rodgers said: "The latest was that there was an offer to take him on loan but that's something that hasn't been discussed any further."
Rodgers has already brought in four players since the end of last season, with Mignolet, Manchester City defender Kolo Toure, Celta Vigo forward Iago Aspas and Barcelona B midfielder Luis Alberto.
But he is still on the lookout for more.
"There are obviously certain areas of the squad where we're a bit thinner than others," he said.
"We probably need a wee bit more support at the top end of the field and that's something we'll look out for.
"That'll be mixed with needing cover in the left-back position -- that's something we're looking at. And we want that extra bit of quality at the top end of the field."