The former Spain national team head coach has come under fire in recent weeks following Madrid's below-par start to the 2018-19 season.
Things went from bad to worse for Madrid over the weekend, as Lopetegui's side were beaten 2-1 by Levante at the Bernabeu, a result that means they are on their worst run in the league after nine matches in 17 years.
That has seen the likes of Antonio Conte and Arsene Wenger linked with the top job at Madrid, but Mourinho insists he is focused on United, and is hoping to stay at the club until 2020 and potentially beyond.
When asked about the possibility of returning to Madrid, where he was previously in charge between 2010 and 2013, for a second spell, he said: "No. My future is here - I have a contract and until the final of my contract I only think about Manchester United. I am happy to stay here longer than that."
Lopetegui has remained defiant despite the calls for him to be sacked, insisting that he will continue to "fight" as Madrid face up to a run of five matches without a win in all competitions.
Goal understands that Madrid are looking at possible replacements for the 52-year-old, although he is expected to still be in charge for Sunday's Clasico meeting with Barcelona, where the result is likely to determine whether he will be sacked or not.
Scoring goals has also been a problem for the Champions League winners this season, with Marcelo's second-half strike against Levante their first since September 22 - the second worst scoring run in their entire history.
Mourinho, meanwhile, has seen his own job called into question after a disappointing opening to the new campaign.
The Red Devils find themselves in 10th place in the Premier League table, with Mourinho's side claiming just one win from their last six matches in all competitions.
And next up is a potentially daunting Champions League fixture against Juventus, where Cristiano Ronaldo will make his second appearance at Old Trafford since he left the club back in 2009.