Rangnick has failed to galvanise an under-performing United squad since replacing the sacked Ole Gunnar Solskjaer in November.
A 1-1 draw against Chelsea on Thursday left the Red Devils still five points adrift of the Premier League top four having played two games more than fourth-placed Arsenal.
Rangnick’s initial deal included a two-year consultancy position, but doubt had been cast on his future as he is yet to speak to incoming United manager Erik ten Hag.
Reports in England on Thursday claimed Rangnick could sign a deal to become Austria boss within the next 48 hours.
However, he revealed he has permission from United to marry his consultancy role with another job.
“Let’s speak tonight about Manchester United,” said Rangnick when asked about his links to the vacant position as Austria manager.
“I can confirm I will definitely continue in my consultancy role. We have definitely agreed now on the content and time of my consultancy role.
“It would leave space for another job, but that is what we agreed in November.”
There was little sign of encouragement for Ten Hag from another limp performance as Chelsea failed to make the most of their dominance at Old Trafford.
Marcos Alonso’s opener for the Blues was quickly cancelled out by Cristiano Ronaldo in the second half.
But a point does edge Chelsea closer to securing their place in the Champions League next season.
Thomas Tuchel’s men move eight points clear of fifth-placed Tottenham with five games remaining.
“If there is one team that deserves to win it’s us, but we didn’t take it,” said Tuchel.
“It’s our responsibility to win a game like this when we dominate in all areas of the match. We were not decisive or clinical enough.”
The broader scale of the problems at United were demonstrated by another supporter protest against the club’s owners, the Glazer family.
Many fans remained outside the stadium until the 17th minute in a sign of protest at the 17 years since the Americans took control of United with a leveraged takeover.
The late arrivals did not miss much as Chelsea were just the latest side to have too much energy, ideas and organisation for a United team that can now only match their lowest ever points tally in the Premier League era by winning their remaining three games.
In keeping with the Red Devils’ season only David de Gea and Ronaldo emerged with any credit by keeping the hosts in the game at either end.
De Gea spread himself brilliantly to twice deny Kai Havertz with the best chances of the first half.
Tuchel was furious with his German compatriot’s poor finishing, but Havertz did at least have a hand in the goal that finally put the visitors in front on the hour mark.
Havertz flicked on Reece James’ cross into the path of Alonso, who hit a sweetly-struck volley across De Gea.
The lead lasted just two minutes as Ronaldo was at his clinical best to smash home United’s first big chance of the game.
Nemanja Matic chipped a brilliant pass into the path of the Portuguese to control and fire high past Edouard Mendy for his 23rd goal of the season.