They are third in the standings with 18 points from 10 matches, a point behind City in second; both teams are well behind leaders Arsenal (25 points).
The Merseyside club endured a torrid spell in October during which they lost six of seven games in all competitions, but they appear to be out of the doldrums after beating Aston Villa and Real Madrid, keeping clean sheets in both games.
Szoboszlai, of Hungary, said Liverpool had shown a tenacity in their hard-fought 1-0 Champions League victory over Real Madrid on Tuesday that they had previously been missing.
"Everybody could see against Real, all of us running, fighting, being there for each other, covering each other's backs," he told the British media on Friday. "The most important thing is to keep going like this."
"There is a long way to go. Now it's all about the Premier League and facing City at the weekend. We know how good they are now. The season is long. If we were seven points clear at this stage, nobody would be saying that we had won the league already."
"Last season, when we were leading the way, we just stayed calm and kept on going because anything can happen. We just need to focus on ourselves, win our games and then let's see what other teams are doing."