Since taking over as England manager in 2016, the former Hazelwick schoolboy has guided the national team to a World Cup semi-final and the European Championships final.
A petition for a statue in the town was started in 2018 by Spotted: Crawley's Daniel Armstrong. And pressure on Crawley Borough Council to do something has mounted with leader Peter Lamb saying last week they are considering options.
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And Mr Smith tweeted before Sunday's final said: "We already have a Southgate neighbourhood, but should the new Town Hall be named after Gareth - our proud son of #Crawley - or should their be a statue instead?!"
And the vote saw 66.7% go for a statue over 33.3% who wanted to name the new Town Hall after Southgate.
After the final, Mr Smith told the Crawley Observer: "Crawley can be very proud that Gareth Southgate took England to the final of a major tournament, the first time the national men’s team has managed this in 55 years.
"It’s right for our community to discuss how we can best commemorate Gareth’s work.
"The suggestion of a statue is one worthy of consideration, and with a new Crawley Town Hall due to open in the near future perhaps it would be appropriate to name this building after Gareth who has led our national team with such distinction."