We reached a general agreement with Manchester United on the transfer of Jadon Sancho, pending full completion, as there are still some formalities to agree on and the medical check to be completed.
"We want to fight for trophies," Rodgers told a news conference. "If we could become a sustainable club in European football, that shows we're successful. Commercially, we're 10th. For budget, we are eighth.
"It will be difficult to compete with clubs three or four times our budget but it doesn't stop us fighting. The lowest we will finish is sixth this season."
England captain Kane's future at Tottenham has been the subject of intense speculation with the club failing to qualify for next season's Champions League.
"I'd be lying if I said I didn't (want the Premier League record), I think if I get to the end and I haven't broke that record and the Wayne Rooney England record (53 goals) then I'd probably be a little disappointed in myself," he said.
Aguero has won 12 major trophies with City -- including the club's first Premier League title in 2011-12 when he scored an injury-time winner on the final day of the season.
"Tomorrow we'll decide," Guardiola added. "As much he can play he will play. He's been disrupted, he had a partial training session."
Harrison doubled United's advantage on the hour mark, getting a foot to Ezgjan Alioski's powerful drive through a crowd of bodies after a corner, to flick home past Peacock-Farrell.
"In the first half we insisted until we managed to score. We defended well," United manager Marcelo Bielsa said. "In the second half we didn't defend as well, but were efficient and managed to score."
Violent protests against United's American owners, who were central to plans for a breakaway Super League, led to Sunday's Premier League match at home to Liverpool being postponed.
Responding in an open letter to Fans' Forum members, Glazer said: "As one of the few European football clubs listed on the public markets, we believe in the principle of fans owning shares in the club.
"Let me try to win at Crystal Palace... United is an extraordinary team arriving in the last two months in their best form of the season and we need five points to be champions," Guardiola, whose side beat Paris St Germain 2-1 in the Champions League in midweek, told reporters on Friday.
"All we can do now is recover as well as possible from the physically and mentally tough game we played in Paris. It is our sixth game in a row away. It is a lot of travel and we are tired in many aspects.
"The Premier League is considering all actions available to prevent it from progressing, as well as holding those Shareholders involved to account under its rules," the league said after a shareholders meeting to discuss the Super League proposal.
"The Premier League would like to thank fans and all stakeholders for the support they have shown this week on this significant issue.
"Of course we will never give up," Solskjaer told a news conference. "Man United will never, ever give up. This team, this club has had too many setbacks, too many great comebacks to have that in our DNA.
"You have got to make progress and that is the reality," he said. "You want to finish the season strongly and if we manage second then it is progress.
Cavani, a free agent after leaving Paris St Germain as their record goalscorer, found no suitors until United stepped in after failing to land Erling Haaland and Jadon Sancho last year.
"Injustice never wins," Cavani said as the victory sealed United's ninth comeback win in the league this season, sparked by his excellent performance that helped ensure United remain unbeaten away from home and seven points above third spot.
"It's part of the game. In the last 10 minutes they had other chances. They are fast and can do it. When they defend in the way they were doing, you have to stop them running," he said. "We didn't do that.
Argentine Bielsa, who steered Leeds back to the top flight after a 16-year absence this season, described Guardiola as a magical man and said he had given up trying to emulate the Spanish coach's style of play.
Guardiola, who previously hailed Bielsa as one of the most important influences on his trophy-laden managerial career, was quick to return the compliment.