Guarin has been heavily linked with a move to Chelsea in recent weeks and Inter have claimed that there were discussions with the Premier League club.
However, the Serie A club have decided to hang on to the Colombian midfielder, who recently confirmed he is happy at the San Siro.
"Guarin is an Inter player and we are happy to keep him," Inter's sporting director Piero Ausilio told Sky Sport Italia before Monday night's game away to Lazio.
"Denying the contacts with Chelsea would be denying the evidence. It is a source of pride to talk with them about one of our players, but everything stopped there.
"We are happy Guarin could stay with us for a long time. We don't have the intention to sell him. He's an important player."
Recent reports have also linked Inter with an approach for Osvaldo, who only left Serie A last summer to join Southampton from Roma.
Osvaldo has scored three goals in 13 Premier League appearances for Southampton, but Ausilio has scotched talk of a loan deal for the Italy international.
He added: "We have never had any idea for Osvaldo. In attack, we will remain as we are."