Terry stopped short of handing in an official transfer request
but the central defender is determined to speak with City officials
over the proposed move.
The move comes 48 hours before Carlos Tevez flies in to
Eastlands for a medical to seal his £25million switch.
Abramovich is desperate to keep Terry but the England captain
wants his future resolved before Chelsea leave for their pre-season
tour of America on Thursday.
The pair met after Terry and the rest of the first- team squad
took part in an event to support Chelsea's charity partner for the
season, Right to Play.
After spending the afternoon at Wentworth, Terry slipped away to
talk with the Russian billionaire in a meeting that lasted more
than two hours.
Chelsea are reluctant to let Terry leave for City, even for an
astonishing £50m. But the defender is determined to hear what they
have to offer.
City chief Mark Hughes is prepared to fly back from the club's
pre- season training camp in Germany to convince the England
captain his future is at Eastlands.
Terry, 28, will be offered £280,000 a week plus a £5m signing-on
fee if Chelsea give them permission to talk.
There are already plans at City of setting up a John Terry
Foundation, similar to the project proposed by the club during
their pursuit of Kaka in January.
City's new partnership with Umbro, who also hold a lucrative
contract with Terry, is seen as crucial to the deal.
Although the defender has told friends it would be a huge wrench
to leave Chelsea, he fears they have regressed after the
big-spending era under Jose Mourinho.
He is also aware of talk at Stamford Bridge about the proposed
transfer fee from City being used to complete the signing of
Alexandre Pato from AC Milan for a similar fee.
Milan are in talks with Sevilla over the arrival of Brazilian
striker Luis Fabiano and will let Pato leave for Chelsea if they
can conclude negotiations with the Spanish club.
Terry has become increasingly disillusioned at Blues and is
concerned that they will not be able to challenge Manchester
United's domestic dominance next season.
Although Chelsea spent £18m signing Yuri Zhirkov, the only other
arrivals are Middlesbrough keeper Ross Turnbull and Manchester City
striker Daniel Sturridge.
Terry had been convinced after talks with Abramovich before the
FA Cup final victory in May that David Villa and Franck Ribery were
the club's two top targets but they have admitted defeat in their
pursuit of both.
City are the up- and-coming team in English football with big
bucks to realise the ambitions of super-rich owner Sheikh
Mansour.
Terry believes City are just two players short of competing with
Arsenal for a Champions League place.