It was announced on Tuesday that Salah and Liverpool will part ways at the end of the season.
A move to Saudi Arabia has been mooted for the Egyptian great, however Sims says NYCFC are also keen.
Speaking at the Sports Business Journal Business of Soccer conference, he said: "I would love to have Mo Salah.
"We have not had any discussions with him or his people. What is most important is does the player want to come to MLS and be in New York City.
“We are not going to go out and sell someone on New York, the league or our club. We want players who really want to be here.
"And the other thing about star players is you need to make good choices... You need the guys who are going to be the hardest trainers, good team mates and good for the locker room and the culture. We do a lot of due diligence, and not just on star players."
Interestingly, NYFC are part of Manchester City owners City Football Groups stable.