The former Juve boss' future is in doubt despite guiding Inter to their most successful season since 2010-11
Antonio Conte and Inter look to be heading for a divorce, much to the disappointment of a long-serving former Nerazzurri president.
The 3-2 Europa League defeat to Sevilla on Friday meant head coach Conte finished without a trophy in his first season with Inter.
It appears increasingly likely to be his last campaign at the club, with former Juventus and Italy boss Conte casting doubt on his future after the game by saying Inter must plan for life "with or without me".
Conte said that "something happened" and also pointed to family commitments, questioning whether football should be his priority.
Ernesto Pellegrini, who was president of Inter from 1984 to 1995, indicated he would rather Conte be encouraged to enter a second season than leave now.
Inter finished second in Serie A, reached the Coppa Italia semi-finals and savoured their European run, amounting to their best season in almost a decade.
"I hope that everything can be resolved. If he intends to leave, it will inevitably happen but I hope it does not," said Pellegrini.
"Of course it is a question of taking Conte and asking him what he has in mind, the reason for this outburst that I don't understand.
"We fans are happy with the results. Of course if we had won the cup it would have been a pinnacle, but it wasn't to be and we move on."
Speaking to Radio Sportiva , Pellegrini said: "Everything is in place for a season of excellence next year."
He also spoke of the possibility of former Juventus boss Massimiliano Allegri being a potential replacement for Conte.
That has been widely reported in Italy as being a plan Inter have in place, with Conte and current president Steven Zhang said to be poised for a meeting early next week.
"I really like Conte. Don't get me wrong, I also know Allegri very well and have a good relationship with him," Pellegrini added.
"Presidents come and go, coaches come and go, the club remains: the right solution will be found for us fans who have always loved this team."