Is NFL free agency like the NBA in terms of the team that drafts you can offer you more money than any other team?

An example would be, in the NBA the team that drafts you can offer you a $200m contract extension a year or 2 before your rookie deal is up (it will kick in after your rookie deal is up) and the other NBA teams can offer you no more than $175m if you were to wait the 1-2 years and hit unrestricted free agency. Is it like that in the NFL?