The news that AlphaTauri driver Gasly would replace Alonso, who is joining Aston Martin, was announced over the Japanese Grand Prix weekend.
Szafnauer was asked how the decision to hire Gasly had come about, he replied: "Well, we had, as everyone knows, we had a seat available around the summer break, and then we started looking around as to who would be a best fit, and we had some criteria to work to," Szafnauer said.
"And the three things we wanted was naturally speed: a fast driver; one with experience and also youth at the same time. Adding all three things up, there aren't many people that have all that and Pierre definitely does.
"We thought he was a great fit for us. So, we put him on our shortlist, and then went about getting it done."
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The Alpine boss was then asked when they started looking for Alonso's replacement, Szafnauer answered: "It was maybe a week or so. Not even. I mean, shortlist first.
"When it looked like Oscar (Piastri) wasn't 100% certain with some of the contractual issues that we had, then we started working on a shortlist of who else it could be, and Pierre was on it," he added.
Daniel Ricciardo had been linked to joining Alpine at one stage, and Szafnauer admitted there had been a list of drivers that were discussed.
"Well, you know, at the beginning we discussed with a few drivers, including Daniel and, you know, Pierre meets the criteria that I said to a tee.
"He's experienced fast and young. So, when it became evident that Pierre was a possibility, we made our shortlist even shorter," he said.
Gasly's new teammate will be Esteban Ocon and two drivers are known to have personal issues with each other, but Szafnauer said the whole Alpine team were all excited and on the same page about the Frenchman joining.
"Yeah, I mean, we made an informed decision. And that means talking to the entire team, including Esteban beforehand, to make sure that if we did make a decision, it's a team sport and we have to be able to work together and optimise.
"And Esteban was very supportive, Pierre as well," Szafnauer explained. "They're professionals and they have no issue working together. And hopefully, the friendship will rekindle.
"They were friends at one point, but from a professional perspective, they're both very happy to work with each other," Szafnauer added.