Madrid go into the City game having won just one of their last five matches in LaLiga, including Sunday's 2-0 home defeat to Celta Vigo at the Bernabéu.
ESPN reported on Monday that president Florentino Pérez met with the Madrid board after the Celta loss to discuss Alonso's future, with concerns over his management and the performances of key players.
"Yes," Alonso said, giving a one-word answer when asked if felt he still had his squad's support, in a news conference on Tuesday.
"The team is united, the team is convinced," Alonso said earlier, when asked about the situation going into the City game. "Everyone is convinced we can win tomorrow. Nobody has doubts. But for that, we have to play with a good rhythm, intensity, and compete."
Speaking later, midfielder Aurélien Tchouaméni said that Madrid's disappointing results -- which have included a 1-0 Champions League defeat at Liverpool, and three draws at Rayo Vallecano, Elche and Girona, before the Celta loss -- were not Alonso's fault.
"In the Vigo game, for sure the coach had a good game plan," Tchouameni said. "But in the end, we the players are on the field. If we're at our level, we have more chance to win these games. If we lost 2-0, there's a problem for us on the pitch, with the intensity. It isn't the fault of the coach."
Madrid's poor form means they are now four points behind Barcelona at the top of LaLiga, despite having beat their rivals in October's Clásico.
ESPN reported on Monday that Zinedine Zidane and reserve-team coach Álvaro Arbeloa are two names being considered to replace Alonso.
"As Real Madrid coach you have to be ready to deal with these situations with calm," Alonso said, when asked about the speculation. "That's how I feel. I'm excited about what's next, starting tomorrow, after the anger there was [after Celta], which is normal. Now we're thinking about City, the Champions League. Things can change quickly in football."
Sources have told ESPN that Alonso's handling of the dressing room is now being questioned by club executives.
"It's not about changing, it's about adapting," Alonso said, when asked about his arrival as coach last summer from Bayer Leverkusen. "I know the culture at Real Madrid, that's why it's the biggest job in the world, you need to adapt, you need to learn. There's a process, an interaction with the players. Some days are good, some days are not so good."
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Tchouameni admitted the team "have to improve."
"If we don't play with the maximum intensity, it's very hard to win games," the France international said. "We have to understand that to win these games we have to give our best. We didn't against Celta, and we have to tomorrow."
Alonso said he didn't regret the high-profile decision to substitute Vinícius Júnior in the Clásico, which drew an angry reaction from the player -- saying "what I see on the pitch is the decision I have to take," -- and said he would be open to working in the Premier League in the future.
"At the moment, this is my place," Alonso said. "This is where I want to be. In the future, you never know what could happen."
