Manchester City have fallen 14 points behind the leaders at the half-way stage of the season with Liverpool also having an outstanding game against West Ham United.
The Citizens have been drawn against 13-time European champions Real Madrid in the round of 16 stage of Europe’s premier club competition, which continues in February.
Manchester City have never won the Champions League; the closest they have come was the semi-finals in the 2015/2016 season when they eliminated by Los Blancos.
Guardiola has won the Champions League twice with Barcelona but is yet to win it with another club since his last triumph with the Blaugrana in 2011.
With hopes of a third straight league title fizzling away, Xavi believes his former teammate, who later became his boss, will trade domestic glory for continental success.
"Pep is a born winner," Al Sadd head coach Xavi, who played under Guardiola at Camp Nou, told The Mirror.
"It will hurt him that Manchester City are so far behind Liverpool in the league - and he won't give up.
"He will be realistic though. The gap is a big one and at the moment it doesn't look likely that they can make it three titles in a row.
"With that in mind, I think there's a big chance Pep will prioritise the Champions League.
"They will be two big games coming up against Real Madrid - and maybe there will be a chance to rest players before these games that they wouldn't have if they were in a title race.
"Pep will want to win every trophy that he can - but if you'd asked him at the start of the season what he would prefer, I'm sure he would have said the Champions League.
"He joked with Klopp that maybe Manchester City and Liverpool should swap trophies this year - but there was some truth in that joke, I think.
"He's won every trophy in England with Manchester City and he knows that winning the Champions League with them would take them to the next level as a club."
