Serie A champions Roma are thought to be admirers of the highly-rated custodian and preparing a move for him.
The Giallorossi are thought to be ready to offer Chelsea Argentine superstar Gabriel Bastituta in a swap deal to tempt the West London side to part with Cudicini.
The 28-year-old has been in sparkling form for Chelsea this season with a number of eye-catching performances.
Cudicini joined The Blues from Castel Di Sangro in the summer of 1999 and has established himself as number one under Claudio Ranieri.
The former Lazio and Milan ace has beaten off competition from Ed de Goey and Mark Bosnich to become a regular in the Chelsea side.
The Italian shot-stopper has attracted a lot of interest with 15 clean sheets and further enhanced his reputation with a superb brilliant penalty save from Marcus Bent in Monday's draw against Ipswich for his third penalty save of the season.
Roma are looking for a new goalkeeper with Francesco Antonioli and summer Ivan Pelizzoli failing to convince in goal this season.
Chelsea could be tempted by the offer of long-term transfer target Batsistuta, but Cudicini wants to stay at Stamford Bridge and get a new deal.
"I have not heard of anything but rumours are always flattering to a player," Cudicini told The Sun.
"At the same time, I hope my performances for Chelsea will result in a longer contract than the one I signed.
"Should they sell me, it will make a handsome bargain. But I would rather stay at Chelsea."
Meanwhile, Chelsea's turbo-charged winger Jesper Gronkjaer is set to miss the weekend game with Everton after picking up an ankle injury in the recent win over Derby.
The Danish wide-man sat out the 0-0 draw with Ipswich over the weekend and coach Claudio Ranieri will hope the injury-prone star recovers as the club push for a Champions League berth.
