Somewhat ironic, given the fact that your first attempt was this:
Anyway, talks about contract extensions can easily take time, like De Gea's contract, where Mourinho stated in august 2018 that De Gea was close to signing it, didn't happen until september 2019. Talks were held in order to find out what Herrera was looking for, amount of years and wages, and you try to reach a compromise, at 29 signing his last big contract it's hardly a shock that he's being shopped around, he's always going to be interested in hearing what others will offer him and it's no surprise that we were never going to go close to matching PSG's offer.
As to why we bothered to make a formal offer when we knew he was unlikely to sign it,
no idea, maybe a last ditch attempt.
Shame he left.