On-field success alone may not be enough to keep coach Antonio Conte at Inter, Ivan Cordoba believes.

Conte has guided Inter to the top of Serie A and they moved four points clear on Sunday with a 3-0 win at rivals Milan, the pace-setters for much of the season.

Not since Jose Mourinho's treble-winning season of 2009-10 had the Nerazzurri won the Derby della Madonnina by a three-goal margin or greater, with this latest result boosting hopes of ending the wait since that campaign for the Scudetto.

Yet even if Inter can secure the title this term, former club stalwart Cordoba - a five-time champion, including under Mourinho - still harbours concerns over Conte's relationship with the board.

The ex-Juventus, Italy and Chelsea coach has had difficulties with some of his former bosses and at one point appeared set to leave San Siro last year, just one season into his Inter reign.

While Cordoba is encouraged by Conte's work since then, he is not yet sure of a long-term plan.

"I don't know what Conte is thinking," Cordoba told Stats Perform News. "I can only hope he can achieve something important for Inter. He is on the right path.

"But since I have been part of that group for a long time, I can say Conte wants to build something not only on the pitch but off it too. These aspects are pivotal.

"You can't win or keep winning if you don't look after parallel details and fix them with the board along the way.

"We know this because Conte spoke about it before the beginning of this season.

"Now the most important thing is the pitch, because without being successful there you won't get anywhere, but the other side of the job is pivotal too.

"If himself and the board share common ideas and intents, he could be at the club for a long time. If he doesn't, it is unlikely."

Inter host Genoa in their next match on Sunday, ahead of Milan's potentially tricky trip to fourth-placed Roma later the same day.