The Toffees are prepared to offer the veteran midfielder a three-year contract, which is something the other interested sides are unlikely to match.
Lampard would be earning around £80,000 per week during the first year of the deal, although his wage would decrease in the second and third season.
There have been reports that Chelsea officials have changed their minds and are prepared to offer the England international a contract renewal, but the reality is Lampard will become a free agent at the end of the season.
The 34-year-old is also being linked with a move to LA Galaxy, who want him as a replacement for David Beckham.
Lampard remains the highest scoring midfielder in English Premier League, having scored no less than 160 goals in 539 league appearances.