Sampdoria striker Quagliarella – the top scorer in Serie A this season with 21 goals – became the oldest goalscorer in Italy's history when he netted in their Euro 2020 qualifier against Liechtenstein on Tuesday.
Aged 36 years and 54 days old, the Sampdoria forward scored a 35th-minute penalty, putting Mancini's side 3-0 up.
The game saw Quagliarella make his first competitive international start since a World Cup qualifier against Cyprus in October 2009 and Mancini is convinced he can continue to provide a viable option for the Azzurri in their Euro 2020 qualifying campaign.
When asked if he would make the squad should Italy qualify for the tournament, Mancini said: "I cannot say that at this moment.
"He is in great shape right now but it's hard to make a prediction for June 2020. It's difficult to say what it can happen.
"He is a serious professional and I believe he can keep this standard until then. He is for sure a striker that knows how to play football and can add something to our game obviously."
Quagliarella was named in the squad ahead of Mario Balotelli, who said last week that he might refuse future call ups to the national side.
Mancini, though, has suggested that the Marseille striker needs to improve his fitness if he is to work his way back into contention for Italy's next qualifiers against Greece and Bosnia-Herzegovina in June.
"Mario needs to stay calm and improve his physical shape," he added. "He is already progressing in this aspect.
"He's in an important player and a public figure so it's normal that people talk about him.
"I repeat he has to stay calm and work hard. This has to be his only focus for the coming months."