The Scottish champions are reportedly keen to recruit the 29-year-old midfielder as manager Gordon Strachan attempts to bolster his squad for the season ahead.
Delvecchio is also attracting interest within Italy. Palermo and Napoli are believed to be the Hoops' main rivals for his signature.
Celtic have already moved to recruit SPL stars Scott Brown, Scott McDonald and Chris Killen as they bid to retain their crown next season.
And talks are expected to take place with AC Milan winger Massimo Donati this week.
But Parkhead chiefs have yet to table a bid for Delvecchio, who comes with a five million euros (around £3.3million) price tag.
A source at the Serie A club said: "The position of Sampdoria regarding Gennaro is quite simple - there has been no official contact from Celtic yet.
"There has been no contact from Palermo either. Until there are official offers, there is only rumours.
"I don't know if he would prefer to move to Scotland or remain in Italy.
"He is still our player at the moment and, once we receive an offer, we can discuss it with him then."
Meanwhile, Celtic were expected to run the rule over Dutch striker Maceo Rigters in the semi-final of the UEFA Under-21 Championship against England in Heerenveen.
The NAC Breda forward, 23, is understood to be high on Strachan's summer wish-list and has also been linked with a move to Newcastle.
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