Both players sustained their injuries in Sunday’s 1-1 home draw against Chelsea.
City sit second in the league on 42 points, six behind leaders Arsenal after 20 matches.
"Dias, hamstring for four to six weeks," Guardiola told reporters ahead of Wednesday's home game against 10th-placed Brighton & Hove Albion. "Gvardiol out for a long time.
"(John) Stones, no idea. Not ready for the next games. (Nathan) Ake fine.
"With the spirit that we have, always we can cope. Considering fatigue, we have to see the faces and take a decision tomorrow. Tomorrow we will see."
Asked if City will enter the January transfer market, Guardiola said: "Maybe we get something, but it is completely different (to last season). We are not going to buy four or five players like last season."
City have been linked with Bournemouth winger Antoine Semenyo and Crystal Palace centre back Marc Guehi.
Best wishes for Amorim
Ruben Amorim's turbulent 14-month tenure as Manchester United manager ended abruptly on Monday when he was sacked a day after passionately defending his role and vowing not to quit following a disappointing 1-1 draw with promoted Leeds United.
Chelsea coach Enzo Maresca also departed after an apparent fallout with the club's leadership.
Asked whether managers are being given less time to prove themselves, Guardiola replied: "Yes, it's a fact. Less time. Like what happened with Enzo.
"I can't say anything out of respect for the players and the institutions of Chelsea and Manchester United.
"All I can say is Ruben is a top manager. The decision has been made by our neighbours, but I wish Ruben all the best for the future."
