The Jambos host United at Tynecastle after drawing 1-1 at Ibrox last weekend and 1-1 in their Europa League third qualifying round first-leg fixture with Paks on Thursday night.
Jefferies told Hearts' official matchday programme: "The secret is if you pick up points against the Old Firm then you have to handle everybody else right.
"United had a tremendous season last time and pushed us close for third place.
"They have lost one or two (players) but have recruited well, a bit like ourselves, and this is going to be another tough match.
"We are coming into the game off the back of a European tie in Hungary which is never easy but we just have to handle it.
"United might have been in the same boat but were unfortunate to go out to a decent side.
"This will be another tight match and both teams will be eager to put on a good show.
"Hopefully we can follow up the good work from Ibrox and take another confidence boost by producing most of the form we showed against Rangers."
David Obua scored as Hearts took a first-half lead at Rangers, who levelled in the second half to deny the capital club all three points.
Obua's goal came from a Danny Grainger corner and the Ugandan revealed he was acting under the instructions of Hearts goalkeeper Marian Kello.
Obua said: "We were trying to find a way of beating the zonal marking and Marian told me I should take up the position I scored from.
"He insisted it was a good position to come in from and attack the ball and to be fair to him that is what happened.
"It was great to see it go in and while we could have won the game I'm pleased we got a point in the end."
Meanwhile, striker Kevin Kyle, who has been out since January with groin/hip problems, is targeting a return in the August 28 Edinburgh derby with Hibernian.
He said: "I've pencilled in a wee game against Hibernian at the end of August, so that would be ideal - perfect really - if I was back for that one.
"If I could come on and do what I do best, score a last-minute winner, then I'm sure everybody would be happy with that and hopefully forget about the last six months."