"Because the demands are so high - obviously being a rookie - teams don't want to go long-term too early because they don't know how you're going to go.
"I would like to stay with the team - that would be amazing.
"Hopefully in the next few weeks we can have some news; my fingers are crossed.
Rules limit the amount of development manufacturers can make during the season and it is expected that the Jaguar outfit will be much more competitive when they begin their second season in the category in December.
Evans is expected to be part of that development and is likely to sign a new deal in the next few weeks.
"They want to choose the right people," he said.
"The thing about Formula E is that all of the teams are paying their drivers. There isn't one driver bringing financial backing that you see in Formula 1 so they can choose who they want.
"That is the way racing should be - the best should be chosen on merit.
"Hopefully I have done enough to get myself another contract."
Evans was recently rated the ninth best driver in the category by Motorsport.com and there is a chance he could command interest from one of the more established teams in the field although he wouldn't be drawn into discussion about that.
"Who knows? We'll see. Time will tell," was the former Toyota Racing Series star's response.
Unlike Formula 1 much of the famed silly season or free agency as such takes place behind closed doors in Formula E with a culture of not publicly discussing contract negotiations.
It is expected most teams will set their driver line-up within the next month.
