Jeff Demps could give the Patriots an immediate boost in the return game. (John Raoux/AP)

But Bill Belichick and company may have just solved that deficiency with one late — and very fast — signing.

Jeff Demps, the former Florida running back who helped the U.S. men’s 400-meter relay team claim silver at the London Games, has agreed to terms with the Patriots, giving New England a potentially lethal return man.

In choosing the Patriots, the former Florida running back who opted to pursue track & field rather than a professional football career last spring turned down an offer from the Tampa Bay Buccaneers, as first reported by Fox 13 television’s Kevin O’Donnell.

Demps also spurned a personal plea from New York Jets quarterback Tim Tebow, who tried to recruit his former teammate with the Gators to join Gang Green.

According to the Fox 13 report, the 5-foot-7, 191-pound Demps visited the Patriots on Thursday and has yet to sign his contract. For that reason, New England has yet to make an announcement.

“We don’t have anything to report,” Patriots director of player personnel Nick Caserio told the Boston Herald.

Demps’ agent, Daniel Rose did not confirm the agreement, but told ESPN’s John Clayton that his client should make an announcement later today.

New England finished 16th in the NFL in average yards per punt return last season (8.9 yards) and 29th on kickoffs (21.4).

And despite a stable of talented running backs, Belichick prefers to rely on multiple options with different abilities on the ground. Second-year backs Stevan Ridley and Shane Vereen have the potential to be a featured running back, Danny Woodhead provides pass-catching versatility and rookie Brandon Bolden has impressed in camp. But no one on the roster can match the speed Demps brings to the table, and that alone could earn him a few snaps per game once he learns the playbook.

Demps — who ran on the relay in preliminary qualifying but not in the final — rushed for 569 yards and six touchdowns in his senior season in Gainesville and totalled 2,470 and 23 over his four-year career.

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