The Sun says Jol stunned club chairman Daniel Levy last week by wanting to sell his star striker.
Matters came to a head when Jol hauled off last season's 23-goal top scorer Berbatov during the 1-0 opening-day defeat at Sunderland.
Berbatov reacted angrily to the decision, prompting Jol to seek a meeting with Levy on the following Monday to demand the Bulgarian hitman's sale.
Jol argued Berbatov, a £10.9million signing from Bayer Leverkusen last year, was not a team player and had to go.
But Levy, who has already rejected a bid from Manchester United for the 26-year-old player, insisted that Berbatov is staying.