Ford established himself as coach Stuart Lancaster's top pick with some commanding displays in the Six Nations earlier this year, but an error-strewn performance during a loss to France on Saturday may have re-opened the door for Farrell, feeling his way back to form after an injury-hit year.
"Two weeks ago before the warm-up games it was Ford but things have changed very quickly," said Greenwood, who won the World Cup with England in 2003 playing outside Jonny Wilkinson.
The choice of who Stuart Lancaster picks in the main playmaking role will be crucial to the country's chances of success on home soil with other such as New Zealand and Ireland boasting experienced campaigners in Dan Carter and Johnny Sexton.
Farrell put in a typically-robust performance in England's first warm-up match, a 19-14 victory over France at Twickenham, while a nervous-looking Ford, albeit behind a struggling pack, dropped catches and kicked errantly in the return leg which saw England lose 25-20 in Paris.
England have one more test against Ireland on Sept. 5 to configure their best team before the tournament starts.
"I still believe that Ford gets the opportunity against Ireland...but you can totally understand why Farrell will have his cheerleaders saying you should pick him," Greenwood said.
"He is a cracking animal."
England open the tournament on Sept. 18 against Fiji at Twickenham and Greenwood remains confident the hosts can top a group that includes Wales and Australia, and push through to a potential semi-final against Ireland or France.
At that point, it's anyone's game, said Greenwood.
"Predicting a semi-final in a World Cup is a mug's game. They are notorious graveyards for favourites.
"You only have to look at France beating New Zealand in 1999, Australia beating New Zealand in 2003, or England beating France in 2007."
(Reporting by John Geddie, editing by Mitch Phillips)
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