Paffett, 23, has tested for McLaren and currently drives for Mercedes in the German DTM touring car championship. He won a demonstration race in Shanghai at the weekend.
Mercedes motorsport boss Norbert Haug confirmed that he had been approached by the Swiss team's boss Peter Sauber, who has close ties to the German carmaker.
"They are interested, we'll see where it leads," told Haug before the German Grand Prix. "It's possible he may have a test."
Fisichella joined Sauber this season but has a clause in his contract allowing him to leave for a top team.
Williams, searching for two drivers for 2005, are interested while recent speculation has also linked Fisichella to a return to former employers Renault should that team fail to reach an agreement with Italian Jarno Trulli.
"Obviously there is a possibility that Giancarlo will leave the team so it is natural that Peter will start to look around," said a Sauber spokesman.
"We can go in two directions, an experienced driver or a young one. And if it is a young one then Gary would be a very interesting possibility."
Paffett's compatriot and former karting rival Anthony Davidson, the BAR reserve driver, has also been linked to Sauber after impressive performances in Friday test sessions at grand prix weekends.
The Sauber spokesman could not confirm reports that the team had asked Mercedes for dispensation for Paffett to drive a third car on the Friday before next month's Hungarian Grand Prix.
A testing ban away from Grand Prix weekends is now in force until the end of August and Sauber have hitherto not run an extra car on race Fridays for cost reasons.
Paffett's manager Martin Hines told British weekly Motorsport News that Mercedes might be reluctant for Paffett to disrupt his DTM preparations but there would be talks.
"We've been talking to Sauber and two other teams," he added. "There is immense interest in Gary and Mercedes has now realised what it has under its wing.
"Gary's contract with Mercedes ends this year and I'm 95 percent certain he will be in F1 next year," added the manager.
"I'm not sure whether he'll be racing or testing but I'm confident he'll be able to carve an F1 career once people see how quick he is. I'm confident that a deal is just weeks, rather than months, away."
