The former los Blancos star is confident the Spain Under-21 international has what it takes to become a key figure at the Santiago Bernabeu in the near future
The 20-year-old has been an integral part of head coach Carlo Ancelotti's squad this season after impressing for Madrid's reserves last term.
And Mijatovic - who also enjoyed a period as the club's sporting director - thinks it is just a matter of time before the Spain Under-21 international is a regular on the Madrid team sheet.
"He is on the verge of becoming an important player for Real Madrid," Mijatovic told Cope.
"He is the type of player who could mark an era at Madrid, I have no doubt about that.
"He is a youth player who has the potential to become a first-team regular without any problems."
Jese has netted three goals in 13 appearances in La Liga so far this season, having found the net in the away games against Barcelona, Valencia and Athletic Bilbao.
The Spain Under-21 international has a contract with Madrid until the summer of 2017.