The playmaker is contracted until the end of next season, but Guardiola would love to see the Spaniard - who has previously said he is likely to leave at the conclusion of his deal - stay at City beyond that.
In the wider picture, City have scored 30 goals in seven games this year, all of which have been won, and Jesus says they are hungry for more.
"Liverpool need to beat more than Manchester City if they are to win this season's Premier League title, with the scars of the past 29 years leaving a mark on the club that will only be erased when wait for the trophy this club demands comes to an end".
"The challenge for us is the Premier League, it's number one and the first thing on the mind because it brings so much to the club on a consistent basis".
Another winter storm on the way Monday
A snowstorm will deliver 4-8 inches south of I-96 and 8-12 inches north of I-96 on Monday, with significant impacts to travel. Dangerously cold conditions are possible Wednesday morning with wind chills now forecast to range from -15 to -25 degrees.
Guardiola has stated the importance of every game City will play from now until the end of the season, making clear that his team can not afford to slip up again. Because they are the best.
'Because we want to get to the late stages, and maybe this will make the difference.
City booked their place in the EFL Cup final on Wednesday with a 1-0 victory over Burton Albion, Sergio Aguero's 26th-minute strike sealing a 10-0 aggregate triumph.
"If you analyse the way they can play, they have three or four of the fastest players in the Premier League", Benitez said. Before that we have plenty of fun and games, as we preside over Sam Ricketts taking on his former club, Wolverhampton Wanderers, in the dugout at Shrewsbury, plus Steve Lovell's return to Swansea, after knocking out Cardiff City in the previous round. If you believe it's a handicap, that's a big mistake. Friendly game, win again, play good, prepare well.
"In three days we go there and after that, it's time to think about Arsenal".
"But at the same time I tell them it's a privilege".