The Daily Mail claim Inter will step up their efforts to land Osvaldo by offering Columbian midfielder Fredy Guarin as part of the deal.
The Daily Telegraph earlier this week stated that Chelsea missed out on signing Guarin this month after the Italian club confirmed the player is no longer for sale.
Piero Ausilio, Inter's sporting director, was quoted as saying Guarin will remain at the San Siro with Chelsea believed not to be willing to pay the £15m asking price.
Ausilio said: “Guarin is an Inter player and we are happy to keep him.”
Guarin, 27, has featured in all 18 of Inter’s Serie A games this season, scoring three goals.
For his part Pochttino has again denied any desire to see Osvaldo leave the club.
“He is very happy here, he has been training very well,” he reported.
“He is very expectant to be fulfilling his contract here. He is also expecting the birth of his son and is expecting his son to grow up in England.
“I am very sorry about all these rumours happening right now, but they are just not true.”
When asked whether Osvaldo has suffered from a weight of expectation due to how much club paid for him he reflected: “I don’t think he was an expensive player, I would say.
"If you look at the prices in the market, I don't think he was an expensive player.
"If you look at the price to his quality, he is a cheap player. I don't mean cheap in a negative way, I mean he is value for money.
"The hardest thing has been his adaptation to the league, that has been the most troubling thing and something he has been working on.”