Blues want England midfielder to cover for the Ghanaian, who could miss most of the season with a knee injury, and are willing to pay £1.5m for his services next summer
The Hammers are believed to want to sell the England international to remove his £60,000-a-week off the wage bill as the London side acclimatise themselves to life in the Championship.
However, Andre Villas-Boas’ outfit are only willing to take Parker on loan, paying a fee in the region of £1.5 million to secure his services for the next campaign.
The midfielder played for the Blues for a year earlier in his career before moving to Newcastle United after failing to break into the first team at Stamford Bridge.
Chelsea are not the only club interested in the Hammers captain as Tottenham are also paying close attention to the 30-year-old, but are unwilling to match the £8m valuation.
Parker was West Ham's star player last season, and despite their struggles he was awarded the Football Writers' player of the year award and was also recalled to Fabio Capello’s England squad towards the end of the campaign.
The Blues are also stepping up their bid to bring Luka Modric to Stamford Bridge and remain undeterred in their efforts despite Daniel Levy’s claims the Croatian will not be sold this summer.