City have opened up a 10-point lead over Manchester United at the top of the table and are on course to win a third league title in four years.
Pep Guardiola’s side have won their last 17 matches in all competitions, including 12 in the league, and look unstoppable.
But Solskjaer says his players must try to close the gap on their local rivals to see what City are made of and if they falter under pressure.
“I don’t think anyone would say they’re not going to go for it,” said Solskjaer, when asked if United were still in the title race.
“We’re going to go for a win in every single game we play, of course we are.
“We just have to control ourselves. We’re second and, of course, your ambition then is to not end up any lower than that.
“We’re going to have to get a good run together if we’re going to put pressure on City and that should start on Sunday, of course.”
United host struggling Newcastle tomorrow, with Solskjaer calling on his side – who have 14 games left in the league – to give everything they have until the end of the season.
“Of course it’s relentless, of course we demand we turn up every game and earn the right to win,” said Solskjaer.
“You’ve got to run more than the opposition, you’ve got to want to win more than the opposition, you’ve got to suffer more than the opposition, you’ve got to put your body on the line.
“Every game in the Premier League is high demand and that’s why the players are paid the money they are to perform every time they’re asked to.
“We ask for relentlessness and attitude every single game.”
Solskjaer also said Marcus Rashford knows what he needs to improve on, after the forward spurned two clear chances to score before getting on the scoresheet against Sociedad.
“Marcus is getting better and better and closer and closer,” said Solskjaer. “He’s improving all the time.
“The chances he gets, he gets them because of his athleticism and his movement and he was strong to hold him off for the first one, then the keeper came close to him so that was a hard-ish one.
“The second one the keeper comes out. that’s another one we’re working on and one we had loads of practice on, actually. But he’s improving and I can see that.
“We’re still working and he knows what we want him to improve on, but the goal he scored was a very, very good example on composure and technical quality.”