Rangnick held his first press conference as the new interim Manchester United manager on Friday, explaining his “major target” at the club and revealing his permanent job intentions.
But the German could have become Chelsea boss last season, after the Blues made contact with him following the dismissal of Lampard, before instead turning to Thomas Tuchel.
“At the time, when Chelsea contacted me, they only spoke about the possibility of four months and no prospective of further than that,” Rangnick said at the press conference.
“Here [at Man Utd], we are talking about six and a half months and a two year advisory role.
“If a club like Manchester United contacts you, you cannot possibly turn it down.”
Rangnick also gave his thoughts on the 3-2 win over Arsenal on Thursday, before explaining his desire for his team to “control” games better.
“I have, of course, watched all the most recent games, even before contact from the club. I’m pretty well aware of what’s happening here, and in the Premier League.
“It’s clear the team have abundantly talented players. The major target for me is to bring more balance into the team.
“Even yesterday we conceded two goals and needed three to win the game. We’re conceding too much. It’s my approach to help the team, to get more balance.
“Yesterday’s game was exciting for the fans, but as the coach that is not the kind of game you want every week. I will try to help these outstanding talented players.
“I want to gain control in future games, you have to play proactively. It’s about helping the team play together, team spirit.
“Yesterday, if you compare the two halves it was completely different. Having these unique fans behind us helps… you could see in the second half.
“It’s not easy and I cannot do that within one or two training sessions, or one or two weeks, but it’s about control. That’s the major target.”