The 34-year-old will be a free agent in the summer, and has also attracted interest from a host of other top European clubs, including AC Milan, Paris Saint-Germain, and MLS side LA Galaxy.
Toffees boss David Moyes is willing to offer Lampard a three-year contract at Goodison Park, on sliding-scale wages if he agrees to stay within the Merseyside club's pay structure, which tops out at around £80,000-a-week.
Moyes has already seen the benefits of signing an England veteran who has looked after himself, in the form of Everton captain Phil Neville.
At 36, Neville is still going strong since signing from Manchester United in 2005, and has made 21 appearances this season, including his 300th for the Toffees in Sunday's 2-0 Premier League defeat at Old Trafford.
Everton will face stiff competition for Lampard's signature though, with Red Devils boss Sir Alex Ferguson also keen to land the Chelsea legend.
However, deep down the former West Ham man - who arrived at Stamford Bridge in 2001 - hopes Blues owner Roman Abramovich will make a U-turn and offer him a new deal to stay in west London.