Roberto Mancini followed up Manchester City's emphatic 3-0 win over Stoke City by announcing that Carlos Tevez has informed the club that he now wants to stay with them and forget about the possibility of leaving.

Mancini said he had held several meetings with Tevez during the past three weeks and received assurances that the man who lifted the FA Cup at Wembley on Saturday is no longer contemplating a future away from Manchester.

"He has said he wants to stay," Mancini said. "He's got a five-year contract here and he told me this [that he would stay] before and after the Cup final. I've spoken with him many times in the last 20 days and it's my opinion that he will stay here next season."

Mancini was speaking after Tevez had scored two of the goals that helped take City above Arsenal and into third place in the Premier League. Joleon Lescott was also on target with a second-half header but it was the brilliance of Tevez's goals – a solo effort followed by a 30-yard free-kick – that will be remembered as he moved level with Dimitar Berbatov of Manchester United as the league's leading scorer with 20 goals.

The Manchester City manager's remarks were a surprise, however, coming only three days after Tevez spoke at length about having family issues living in the northern city, saying he would decide in the summer if it is time to move on.

The feeling behind the scenes at Eastlands is that the 27-year-old Argentinian has gradually come round to realising that there may not be any potential buyers for a player who would cost in the region of £50m and currently earns in excess of £250,000 a week. Tevez has been linked with Internazionale, Real Madrid and Chelsea, but the cost implications may be too much even for three clubs of that financial muscle.

"I think he'll stay here and I don't think he will change his mind later [in the summer]," Mancini said. Pressed for his reasons, the Italian added: "We are playing in the Champions League and will probably have a better squad because we can now buy better players."

Tevez had spoken of wanting to move to Italy or Spain because he felt it would be easier for him to have access to his two daughters, who currently live with their mother in Buenos Aires. His relationship with Mancini has been strained at times and he submitted a written transfer request before Christmas.

"We had a problem in December but everyone can change their mind," Mancini continued. "Carlos is an important player. I don't think he'd find another club anywhere where he would be so appreciated. There isn't anywhere where he would get what he has here. He's a fantastic striker and player for us."

With only one Premier League game remaining – at Bolton on Sunday – the win leaves City contemplating a third-place finish for the first time in 34 years, and Arsenal, who travel to Fulham, facing the possibility of having to reach the Champions League group stage through the qualifying round.

Tony Pulis, the Stoke manager, later tipped City to be authentic title challengers next season. "They remind me of Chelsea when José Mourinho was there – a big, strong, physical group of players with good pace and bags of talent. They will be a force next year, a danger to the other teams going for the championship."

Mancini added: "It was a fantastic performance. That wasn't easy three days after the Cup final. For us it was important to get fourth when we started the season, but now we're in third. There's a big difference between that and finishing fourth and having to qualify for the [Champions League] group stage. It would be perfect to finish above Arsenal."