Although City looked in pole position to sign Sanchez when the window reopened in January, they pulled out, reportedly citing financial concerns over the proposed cost of the transfer, with the Chilean in the last six months of his Arsenal contract and set to become a free agent at the end of the season.
United subsequently swooped to land Sanchez in a swap-deal that saw Henrikh Mkhitaryan move the other way to the Emirates Stadium, the Old Trafford club reportedly paying the former Barcelona man up to £500,000 a week for the duration of his four-and-a-half-year contract.
But Mourinho - who extended his United deal to 2020 on Thursday - indicated he does not believe City's insistence that money was the major factor in them pulling out of the race for Sanchez's signature.
"Alexis reminds me a little bit of the metaphor - when you see the tree with amazing oranges at the top of the tree but cannot get there," Mourinho told reporters.
"You say, 'Oh, I got the lower ones because I don't like the ones at the top'.
"But you do like the ones at the top. They're so nice, so orange, so round, so full of juice. But you can't get there.
"So you say, 'I don't want to go there' or 'I didn't like it, I prefer the other ones'. It reminds me of that story."
Jose's new deal runs until at least 2020 - plenty of time for more scenes like this... pic.twitter.com/g77vVJwobs— Manchester United (@ManUtd) January 25, 2018
United were able to offer Sanchez a huge financial package having avoided paying any transfer fee to sign the forward, who hit 60 Premier League goals for Arsenal, but Mourinho again said he does not think money was the major reason for Sanchez's decision to join the club.
"I know that if other clubs did not get him it's not a problem of money, for sure," Mourinho added. "That's not a problem of money.
"How much would Sanchez cost in a normal transfer, as a player with two or three years left on his contract? We look to the numbers now and I would say roughly between £100million and £150million. So you go to the numbers that the club didn't pay on the transfer.
"You go to the numbers the club pays in salaries, which are obviously higher than others, but you put things in perspective. Alexis could have gone everywhere. He had lots of choices. He decided to come here and you have to ask him why.
"I know he has a big passion for football. But we work also, for money. That's the same for every one of us. I know he wanted to play in a different club [to Arsenal], for his reasons, and obviously he wanted to be paid according to his quality."
Mourinho's side take on Yeovil Town in the FA Cup on Friday.