The Chile winger has been strongly linked with a move to European champions Barcelona, but a deal is far from being completed.
Premier League duo Manchester City and Chelsea and Udinese's Serie A rivals Inter Milan are also interested in the 22-year-old, who is under contract with Udinese until June 2014.
"There are no definite agreements regarding Sanchez," Larini told Gazzetta dello Sport. "We have no need to sell the forward, who is improving and can still do better.
"If no agreement is reached, we would be happy (to keep him)."
Larini revealed Inter had inquired about the player earlier this year, but questioned whether they would now be able to afford him.
"Inter asked us about the player back in January," said Larini. "But we did not even begin any type of negotiation because we wanted to keep him at least until June.
"At that time his value was different to what it is now and it has now become difficult for the Nerazzurri to compete.
"They have proposed an exchange of players to be part of the deal, but there are other clubs that are ahead of them right now."
Sanchez, who is valued at 50million euros, scored 12 goals last season to help Udinese finish fourth and qualify for the Champions League.
Udinese midfielder Gokhan Inler has still to agree personal terms with Napoli before he can complete his move to the Azzurri.
The Switzerland international is set to make the transfer this summer in a deal worth an estimated ?17.8 million.
"It is a situation that regards Inler and Napoli as an agreement has already been reached between the two clubs," Larini told Gazzetta dello Sport.
"The deal will only go ahead if the three parties are in agreement.
"The player has yet to agree personal terms and I think that could soon happen.
"Inler and his agent will decide one way or another."
Larini has not ruled out the possibility that Inler, who is under contract with the Friuli outfit until June 2014, could remain at Udinese.
"We believe the player is happy in Udine so we don't exclude anything," he said.
The 27-year-old Inler, who was also a reported target of Juventus, joined Udinese in the summer of 2008 from FC Zurich.
Inler scored three goals in 33 league appearances for Udinese to help them finish fourth in Serie A last season
Source: Team Talk
Source: Team Talk