The Spaniard spent last season on loan at the Serie A club, who are coached by his compatriot, former Reds manager Rafael Benitez.
Napoli have reportedly refused to meet the release clause in Reina's contract, meaning the 31-year-old is back training with Liverpool during their pre-season tour of the United States.
Jones served as understudy to number one goalkeeper Simon Mignolet in 2013-14, making three appearances in the FA Cup.
The Australian could yet find himself relegated to third choice if Reina fails to secure a transfer, but the four-cap Socceroo isn't worried by the prospect of increased competition for places.
"I'm just focusing on getting fit and making sure I'm ready myself," he told the club's website.
"We're all pushing for the same spot, so it doesn't change an awful lot having Pepe back.
"He was part of the club last season, even though he was on loan - he was still contracted to us. It's just a case of doing our job as best we can, getting fit and then what happens will happen."
Liverpool have invested heavily as they seek to replace Luis Suarez and prepare for life back in the UEFA Champions League.
And Jones feels the team's impressive performances last season under Brendan Rodgers have made Anfield an attractive destination for potential new signings.
"Last season, the way that we played and the results that we were getting, people started to realise that we are a big force within the league," he said.
"We dealt with that. It's up to us now to build on it. All the boys are excited after last season. The new boys coming in saw from afar what we were doing and it was probably a big help for the club to be able to sign them and made them desperately want to come here.
"That will only provide more ammunition for the boys to want to go out and show everyone what we can do."
Napoli have reportedly refused to meet the release clause in Reina's contract, meaning the 31-year-old is back training with Liverpool during their pre-season tour of the United States.
Jones served as understudy to number one goalkeeper Simon Mignolet in 2013-14, making three appearances in the FA Cup.
The Australian could yet find himself relegated to third choice if Reina fails to secure a transfer, but the four-cap Socceroo isn't worried by the prospect of increased competition for places.
"I'm just focusing on getting fit and making sure I'm ready myself," he told the club's website.
"We're all pushing for the same spot, so it doesn't change an awful lot having Pepe back.
"He was part of the club last season, even though he was on loan - he was still contracted to us. It's just a case of doing our job as best we can, getting fit and then what happens will happen."
Liverpool have invested heavily as they seek to replace Luis Suarez and prepare for life back in the UEFA Champions League.
And Jones feels the team's impressive performances last season under Brendan Rodgers have made Anfield an attractive destination for potential new signings.
"Last season, the way that we played and the results that we were getting, people started to realise that we are a big force within the league," he said.
"We dealt with that. It's up to us now to build on it. All the boys are excited after last season. The new boys coming in saw from afar what we were doing and it was probably a big help for the club to be able to sign them and made them desperately want to come here.
"That will only provide more ammunition for the boys to want to go out and show everyone what we can do."