Plans for the facility to be built at the Alan Higgs Centre, in Coventry, will be considered on Thursday.
The Sky Blues' youth players use the centre and its programme will get Â£620,000 of Premier League funding for the coming season.
Wasps has previously said the football club could share the proposed centre.
Coventry City says any reduction in the hours its youth players could use facilities, may diminish the status of its development programme in the eyes of the Football Association (FA).
The Sky Blues' lease at the centre expires at the end of June 2017 and an extension has not yet been agreed.
Chris Anderson, Coventry City's managing director, says Wasps' plans for the Allard Way site "might mean an end" for the academy and are among factors which "severely hamper the club generally".
Factors affecting Coventry
Prof Chris Brady, a football expert at Salford Business School, said: "Lack of training time would be a serious, possibly not insurmountable, obstacle.
"The real issue would be a lack of control and therefore, confidence in the future."
He added fans' attendances dictated the club's turnover and its prospects.
"Lower turnover equals lower wage bill, equals lower league position, equals lower attendances in a vicious cycle," Prof Brady said.
Asked if the club may again have to find another home ground because of these factors - after a groundshare with Northampton in the 2013-14 season - Mr Anderson said: "Possibly, but it's too early to tell."
The rugby club's chief executive David Armstrong previously said the Sky Blues had been offered the chance to use the indoor "kicking barn" at the proposed centre when Wasps were not using it.
The plans include three pitches, the indoor pitch, gymnasium, video analysis suite, hydrotherapy recovery area and physiotherapy rooms.
The proposals will be considered by Coventry City Council, which would not comment until after they were discussed on Thursday.
Coventry City's youth academy is under threat if rugby club Wasps gets permission for a new training centre, the football club has warned.