Arsene Wenger's side have lost just one of their last eight matches and are on course to finish in the top four for a 19th consecutive season, having also made the semi-finals of the FA Cup in their attempts to defend the trophy.
With a seven-point gap to Premier League leaders Chelsea to make up and the club's participation in this season's Champions League looking likely to end in the round of 16 on Tuesday, McLintock urged the club to invest financially.
"I think that's the least we should be looking for," the former Scotland international told Perform.
"At least over the last two years, we should have been buying more top-class players and really challenging for the championship.
"Never mind Chelsea or teams like that - Man City - it's time we get back to our status. We've won doubles before and FA Cups.
"It's nice to see us heading that way but I'd like to see it happen a little bit more quickly."
Arsenal travel to Monaco needing to overturn a 3-1 deficit after a stuttering first-leg display at the Emirates Stadium last month.
Monaco's counter-attacking qualities helped the Ligue 1 side build a two-goal platform in the tie despite a number of key absentees, leaving Arsenal with a mountain to climb on Tuesday.
With Arsenal unfancied to progress, McLintock added: "It's going to be very, very tough.
"Monaco came over here with no fear and with four or five players missing. They caught us on a really bad night and I think they deserved to win as we were terrible.
"But I think we'll be a lot better this time, I think we'll go very close but maybe getting three goals back is asking a little bit too much.
"They may freeze and we won't have anything to lose, so it might finish up being a cracking game and hopefully we'll get through."
