The 21-year-old winger had a terrific first season in Italy last year and further burnished his reputation during the European Championship with Denmark.
His performances have led to interest from several clubs in Europe who are considering snaring him away from Sampdoria this summer.
Leeds are in the market for wingers and there are suggestions that the Whites are interested in signing Damsgaard from Sampdoria in the coming weeks.
But Osti is clear that the club are yet to receive a call enquiring about the Dane’s situation at Sampdoria.
Asked about Damsgaard, the Sampdoria sporting director told Il Secolo XIX: “It is not true, we have not received a phone call.”
Sampdoria signed Damsgaard from FC Nordsjaelland last summer and he featured 35 times for the club last season.
He was one of the stars of the Denmark team that made it to the semi-finals of the European Championship earlier this month.
It remains to be seen whether any club make a concrete move to land the Dane this summer.