Roman Abramovich has earmarked the former Manchester United boss in case Conte leaves before the end of the season, according to the Sunday Mirror.
The Italian’s relationship with Chelsea chiefs has broken down during the course of the season as a result of transfer disagreements.
Van Gaal has been out of work since leaving United in 2016.
The 66-year-old was axed by Old Trafford chiefs a day after winning the FA Cup.
He would be up for a short-term stint in the Premier League.
Van Gaal has said: “I’d be interested in a Premier League club where I’d have the chance to get one over on Manchester United.”
However, Van Gaal would only be offered the job until the end of the season if Chelsea are pressed into action.
Conte’s future has been the subject of much speculation in recent weeks.
He has another season left on his contract but could leave at the end of this campaign.
Speaking last month, Conte opened the door to a possible exit.
“I have another year of (my) contract with this club,” he said. “But as you know very well everything is possible.
“In one moment you stay here, in another moment another person replaces you in your job.”
Conte guided Chelsea to the Premier League title in his maiden season at the club.
However, doubts emerged over his long-term future last summer when he signed a new contract but failed to extend the length of his stay.