The Uruguay international is set to make his first appearance for the Reds this summer in Wednesday's friendly against Melbourne Victory, having flown into Australia on Sunday after extended leave following the Confederations Cup.
While he was away the 26-year-old has spoken about the attraction of Real Madrid and his agent Pere Guardiola has told the club the player wants to play in the Champions League but will not try to force through a move.
But that has not affected Suarez, who has returned to training with the same vigour he had last season and Jones said they expect him to stay.
"It's good to have Luis and (fellow Uruguay international) Seb Coates back," he told the Liverpool Echo.
"Most of the boys were joking with him about his Uruguayan (television) advert which we saw on the internet.
"Luis is a bubbly character. You always know when he's about as you can hear him five rooms away!
"He just loves football - he lives and breathes it. You saw him in training here, he's like a little kid. He doesn't want to stop - it's like waiting for your mum to call you in.
"He's that type of character. He's never going to shirk any effort. We don't expect anything less, no matter what's gone on in the media.
"He's the same player we've been used to. Nothing has changed.