Inter Milan president Massimo Moratti has played down speculation over Samir Handanovic, while Dejan Stankovic and Walter Samuel will also be staying at the club.
Keeper Handanovic has been linked to a possible move to Barcelona for a fee in the region of 30million euros (?25.5m).
But Moratti wants the keeper to stay with the Serie A side and has denied the rumours.
He told Inter.it: "I think there is nothing. I read it in the paper too, but I read a lot of things that are not true, I can't deny all of them.
"Should Handanovic remain? Yes."
Another player new manager Walter Mazzarri could draw on is Stankovic, who has cooled growing speculation he could be leave the club by mutual consent after appearing in just three games last season.
The 34-year-old wants to see if he fits into Mazzarri's plans before deciding on his future.
"There is absolutely no truth in that (speculation)," he told Sportal. "As things stand I will start the season with Inter and then we'll see what new boss Walter Mazzarri wants to do.
"A move back to Lazio or a transfer to the MLS? There is nothing. If an offer arrives then I'll think about it, if not then I'll stay another year with Inter."
Meanwhile, the club have announced the contract extension of veteran defender Samuel.
The 35-year-old's deal now runs for another season and Samuel wants to play his part in a successful campaign.
"I hope to repay the club and the supporters' faith that once again believed in me," he told the club's official website.
The 21-year-old centre-back, who is currently recovering from a knee injury, made 37 appearances in the 2012/13 campaign and scored the club's goal of the season against York.
Parkinson said plans to strengthen his squad started immediately after his side's League Two play-off final win over Northampton, but is prepared to wait in order to bring in the right players.
"It's very easy to sign players at this stage of the summer, but they're often not quite the sort of quality that you need," he told the club's official website.
"We're competing with other clubs for players so that means we have to wait and be patient."
He added: "There is a budget in place we have to work with, and I don't want to spend it all too early and miss out on some of my preferred signings just because we weren't patient enough to wait for their signature.
"We've got some offers out there on the table to players and we've tested the water with a few others.
"I should still imagine, however, it will take a couple more weeks."
The 25-year-old, who spent a loan spell with the U's back in 2007/08, was on loan at Aldershot last season, making 37 appearances in League Two.
He signed a two-year deal with the U's with an option for a further year having passed a medical.
"It's a club I have always followed since my first time here," Rose told the club's official website. "They gave me my big break and I am so pleased to be back.
"I feel like I have matured as a player; I was only 19 when I first signed, and I believe I have learned my trade in the years in between.
"There is such potential here and as soon as I heard of Oxford's interest there was only one club I wanted to play for."
