Bagnaia is 30 points behind Yamaha rider Fabio Quartararo, who leads the standings, after winning his fourth race in a row at the San Marino MotoGP.

There are six remaining - raising the possibility that Ducati could issue team orders and use their numerical superiority to thwart Quartararo.

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“We don’t like team orders but, obviously, we also have to think about winning the rider’s championship,” Ducati sporting director Ciabatti told BT Sport.

“We’ve only won once, with Casey Stoner in 2007, a long time ago.

“It is possible. We go to tracks where we will be competitive.”

Ducati have Enea Bastianini, Jack Miller and Johann Zarco among their riders battling for podium spots and race wins.

Gresini Ducati rider Bastianini engaged in a stunning final lap shootout with Ducati Lenovo’s Bagnaia at the San Marino MotoGP, which Bagnaia won.

It was a highly risky duel which might have backfired - and might have convinced Ducati to ask their riders not to repeat the wheel-to-wheel action.

Ciabatti said: “We won’t try any super-aggressive attacks on the last lap if we are first and second, because there is the risk that somebody will crash which would not be good for any of the riders!

“If somebody can win, maybe don’t try on the last corner to pass him. That’s what we need to clarify.”

With six rounds remaining, Quartararo’s main hopes for victory could be at Phillip Island and Thailand.

“In principle, you may be right,” Ciabatti said. “But we haven’t been to Phillip Island for years and our bike has improved.

“The bike has improved to the point where it can be competitive anywhere.”

Ciabatti reflected on Bagnaia’s win at Misano: “We needed to win and put as many bikes on possible [on top].

“The gap is now 30 points. There is still a long way to go but it’s going in the right direction.

“The last lap was more thrilling than we wanted!

“You are so close to disaster in this situation [the last lap].

“We have memories from Argentina 2016 and we don’t want this repeated! Luckily it was okay, and two Ducatis were on the podium.

“When you have a bike as competitive as Ducati last year, the new bike tries to be a bit better. 

“[Bagnaia and Bastianini’s] bikes are similar so it is the rider making the difference.

“The 2023 bikes need to be better because we see Aprilia have made a big step and are fast.”