Ibrahimovic scored twice in the first LA derby between Galaxy and Los Angeles FC, with one of the strikes a sensational long-range effort.
The former Manchester United striker has already appeared on prime time American television, too, sitting down for an interview on Jimmy Kimmel Live.
And Cole, who is approaching his second full year at the Tampa Bay Rowdies, believes Ibrahimovic's personality has already captured the imagination of American football fans.
"He’s had a massive impact. He is a massive player. Massive personality," Cole told Goal. "It is exactly what the MLS needed and I feel like he will have a big impact both on and off the pitch for both the league and the Galaxy. Nowadays, branding and things like that have become very important.
"I think we have a very individualistic culture and the clubs out here they need people of this stature who bring the following they have, to bring even more attention. I think it will be a great lifestyle for Zlatan and I am sure he will love it.
"It is a wonderful way of life and I think the players appreciate the anonymity that the United States offers, to a certain degree at least, compared to the melting pots of Europe and the intensity of the football. That won’t last forever though, that’s for sure.
"The lessons they have learned from the 60s, 70s and 80s when they brought the names over, they are now being smart about it. I think that clever business people are involved. It is going in the right direction and I would advise anyone to come out here."