The proposed double-helix statue would be placed in the middle of Abington Street in memory of the professor, who died in July this year, aged 88.
But borough councillors have warned the statue should be designed to make sure it cannot be used as a climbing frame.
Councillor Penny Flavell (Con, St Crispin) called for a monument to celebrate Mr Crick's achievements before his death and has since spoken to members of his family about the planned tribute.
She said: "It's wonderful that we're going to have something for the man who has done so much for humankind and that we're going to honour him in this way.
"I think a double-helix is very appropriate and I think Abington Street is an ideal location.
"But whoever designs it will have to make sure that it can't be climbed on and it doesn't look like playground equipment."
Professor Crick grew up in Weston Favell and attended Northampton Grammar School between 1925 and 1930.
In 1953, he made the DNA breakthrough – along with US researcher James Watson – which many scientists have cited as the most important discovery in biology during the 20th century.
Northampton Borough Council's executive committee is due to discuss the proposals for the commemorative statue next week.
But the suggestion of a double-helix statue has been welcomed by Francis Crick's relatives in the town.
During a meeting with council leader Phil Larratt (Con, East Hunsbury) last month, his family said he would not have wanted a statue or plaque, but would have liked the idea of the double-helix monument.
The proposed monument would be illuminated at night and be designed to be vandal-proof.
The designers of the monument will be chosen in a nationwide competition, if the plan is given the borough council's backing.
wayne.bontoft@northantsnews.co.uk