Jennings, who rejected the chance to stay with Scottish club Motherwell this summer, has been trying to earn a deal with the Sky Blues for the past few weeks and featured in the second half of Saturday's 2-1 pre-season victory over Bristol Rovers.
The 27-year-old has impressed manager Andy Thorn and discussions are currently taking place between the two parties.
Thorn told Coventry's official website: "I thought he did well at the weekend. Him and his agent are now in talks with the club at the moment.
"I can't tell you any more about it at the moment but he has done well since coming here."