The UK newspaper said the 38-year-old recent retiree was approached about a potential tryout before he left the LA Galaxy MLS franchise.
"The offer came in and he politely said it wasn't right for him," a source told the Mirror. "Perhaps in the next few months he could change his mind."
The NFL might welcome the international appeal of Beckham, whose marketing reach fits the league's plan to increase overseas exposure with multiple game in London and speculation that a franchise could someday relocate.
Several NFL kickers are former soccer players, including Stephen Gostkowski of the New England Patriots and Nick Folk of the Jets, who once trained with Manchester United's club team and has a younger brother on the U.S. National team.