Van Persie joined United from Arsenal in 2012 for a fee of £24million after refusing to pen a contract extension with the Gunners.
Sanchez is likely to take the same path as the Dutchman, and he could make his debut for United away to Burnley tomorrow (3pm).
With the Chilean leaving, Henrikh Mkhityaryan is expected to come the other way as part of a swap deal.
And Wenger has admitted he was more sorry about when Van Persie departed.
“I would say that our fans today know that Sanchez will not extend his contract, and they have accepted that idea,” Wenger said.
“And the fact that it will not be one-way traffic, it will be other-way traffic as well [with Mkhitaryan], so that makes the whole thing a bit smoother maybe, a bit less disappointing.
“We lose a player yes, but we could gain another player of top level as well.
“When it was with Van Persie it was a similar case, in the fact that he had only one year to go.
“Maybe it was the first case where the big players, Van Persie was one of the first cases where a big player didn’t extend his contract and came close to the end of his contract.
“That will happen more and more.
“Because we arrive at a level where the money at stake for players who are free is so big, and the transfers are so big, that the players think ‘it’s better I go to the end of my contract, and if I don’t get the whole integrity of the transfer now, if I get only half, it’s a huge amount of money.”
“We took Van Persie when he played in the reserve team at Feyenoord and we [put in] long work with him.
“And when you get them there to the level and after they leave, of course that is the most painful.”