Ralf Rangnick said he has not ruled out staying on as Manchester United manager beyond the end of the season.
Rangnick was unveiled as interim manager at a news conference at Old Trafford on Friday before taking the reins until the end of the season.
The German is then set to begin a two-year consultancy role in the summer but asked whether there was scope to continue as manager if things go well, the 63-year-old said he could "recommend" that he carries on.
"The people with whom I have spoken so far have been very clear that we're talking about a six month role as a manager," Rangnick said. "We have never spoken about what will happen in the summer.
"Right now, I'm fully aware they might be looking for a new manager. If they will then speak with me about that we will see.
"Maybe if they ask my opinion and everything goes well and we develop the team I might even make the same recommendation to the board that I did at Leipzig twice when I recommended it might be a good idea to keep working with me for one year.
"But this is all hypothetical. We cannot speak about that. For me now it's about winning the next games and this is the major focus."
Rangnick also said he tried to convince Michael Carrick to stay on and has had telephone conversations with United co-chairman Joel Glazer and his predecessor Ole Gunnar Solskjaer on Sunday.
He also joked about reports he will receive a bonus if he convinces Erling Haaland to sign for the club by pretending to flick through his contract.
"Let me have a look, OK £10 million for Erling Haaland, £10m for Kylian Mbappe, £10m for Robert Lewandowski and £10m for Joshua Kimmich," he said. "I mean this is nonsense, of course there are no such clauses in my contract.
"I'm more than happy with the offensive strike power we have here and the offensive players we have here and quite a few of them did not play [against Arsenal].
"[Anthony] Martial only came on in the last five minutes, Mason [Greenwood] didn't play at all. We have so many top players in the offensive department that we don't need to speak about any other players."
Rangnick's tenure will start with Crystal Palace's trip to Old Trafford on Sunday. He will take his first training session at 3 p.m. GMT (10 a.m. ET) on Friday and has already laid out the issues he wants to fix immediately.
"I think it's pretty obvious the team have an abundance of talent, young, talented players, but enough experienced players in the squad," he said.
"The major target for me in the next couple of days and weeks is to bring more balance into the team. Yesterday [against Arsenal] we conceded two goals, we needed three goals to win the game and if you look at the total number of goals conceded, it is almost two on average, per game, and this is just too much."