Suarez joins Liverpool teammates in Australia
The Uruguay striker, 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.
His presence is unlikely to quash speculation that Liverpool will eventually be forced to offload Suarez, who is keen to move to a club playing Champions League football and has been the subject of a rejected Â£30 million (US$46 million) bid from Arsenal.
"I'm relaxed about it," Rodgers told a press conference of the transfer speculation.
"He's an integral part of the squad. He's arrived in great spirits."
Rodgers, whose side beat an Indonesia XI 2-0 in Jakarta on Saturday, is set to sit down with Suarez, who will miss the start of the Premier League season while he completes a suspension for biting Chelsea's Branislav Ivanovic, in a bid to persuade him to stay.
Rodgers earlier told the English press that "the bottom line is he is employed by the club".
"The money goes into his bank at the end of every month, so he should be here."
With Suarez yet to start training this summer, it is unlikely he will figure in Wednesday's 95,000 sell-out friendly against Melbourne Victory at the Melbourne Cricket Ground.
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