Former Hazelwick School pupil Southgate has made history by taking England into their first major tournament final since 1966.
England will face Italy in the Euro 2020 final on Sunday night.
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There have been calls for a statue of the England boss since the World Cup in 2018 and Spotted:Crawley resurrected the petition for it during this tournament.
He said: "It’s being considered. The question is how much do people think is reasonable to spend on it.
"We have a bust in the town hall that cost £18,000 and that was just the head and that was back in the 90s so we have 25 years of inflation.
"What will a full life size statue cost? And particularly if it looks rubbish and that is my big worry - especially if it comes back and looks like that terrible Cristiano statue and that airport."
But Mr Lamb said they are exploring other options and are open to suggestions.
He said: "What we do want to do, as he has already made history, is recognise what Gareth has achieved.. The town is immensely proud of him Lots of people here knew him or know his family.
"There are various ideas of how we can recognise him. So do drop me a line with your suggestions."
People have suggested renaming parks and roads but Mr Lamb said: "It is tricky to rename things especially as we have a major neighbourhood called Southgate.
"But lots of suggestions are coming in and we will do something. It might not be a statue if I can’t be certain it’s not going to look any good."