If Manchester City extend their winning run to 18 games in all competitions at Arsenal on Sunday, United will be 13 points behind their neighbours when they kick off at home to Newcastle straight afterwards.
"I don't think anyone would say they're not going to go for it," said the United boss, who has seen his team drop nine points in their last five games. "We're going to go for a win every single game we play, of course we are.
"We're going to have to get a good run together to if we're going to put pressure on City and that should start on Sunday.
"But, whatever other teams do – City, Liverpool, Leicester, Chelsea, Tottenham, West Brom, whoever – we can't control. We just have to control ourselves. We are in the position we are, we're second and of course your ambition then is to not end any lower than that.
"We can't hide the fact we've dropped off our form a bit. We dropped points against Everton, Sheffield United, West Brom (and Arsenal), points that we feel we deserved more and we should have got more. Newcastle will be a very important game for us definitely."
Solskjaer has no doubt United will meet his demands for maximum effort to push City for the rest of the season.
"Of course it's relentless, of course we demand we turn up every game and earn the right to win," he added. "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."