The Reds face the second leg of their Europa League last-32 tie with Augsburg at Anfield next Thursday, with the score level at 0-0 after the first leg in Germany, before competing with Manchester City in the Capital One Cup final at Wembley next weekend.
Having been knocked out of the FA Cup by West Ham United last month, Milner's side do not have a fixture this weekend, and the former Manchester City man has called on his side to use the extra rest wisely.
The 30-year-old told liverpoolfc.com: "In terms of where we are now, we've got that rest and we have to use it.
"We've got two massive games next week - a chance to progress in [the Europa League] and a chance to win a trophy which doesn't come around too often.
"It's important that we're ready for those two and hopefully we can get two positive results next week."
Victory over Augsburg in the second leg would see Liverpool keep their European campaign alive and also mean that they could retain the hope of qualifying for next season's Champions League by winning the second-tier tournament.
Meanwhile, if Klopp's side beat City at Wembley on 28 February they will have secured silverware at the first time of asking under the German boss, and will win only their second trophy in the last decade.