Jones, who has been inactive the past three games, has told teammates his recovery from a high left ankle sprain he suffered Sept. 25 has progressed, with a final hurdle to be cleared in practice. The Patriots' first practice of the week is scheduled for Thursday.
Coach Bill Belichick has deflected questions on Jones' status -- and his overall quarterback plans -- when asked in recent weeks.
"Hypotheticals and all that, I'm going to stay away from those," Belichick said Wednesday. "We'll see what we are actually dealing with here as we go forward."
Zappe has started the past two games, going 2-0. In 11 quarters of action overall, Zappe is 51-of-70 for 596 yards with four touchdowns and one interception.
In the three games Jones has started this season, the Patriots went 1-2 and Jones was 64-of-97 for 786 yards with two touchdowns and five interceptions.