ESPN Patriots reporter Mike Reiss explains how Adrian Peterson's power running style fits New England so well and what it means for LeGarrette Blount's future with the franchise. (1:55)

FOXBOROUGH, Mass. -- When it was first learned that veteran running back Adrian Peterson was set to become a free agent, his fit with the New England Patriots was viewed as an unlikely possibility.

The main reason was cost. Projecting that Peterson would be commanding a salary significantly more than the veteran minimum, it didn't seem like a fit for a team that seldom extends itself financially at the position. Add in a deep running back class in the draft, and Peterson's challenges in pass protection, and the odds seemed to be even longer of the sides coming together.

Thus, it was no surprise back in early March when an initial media report surfaced that the Patriots hadn't discussed Peterson, and that "it would be safe to assume that the Patriots won’t pursue him."

Sunday's news that the Patriots will be hosting Peterson on a visit, reported by ESPN NFL Insider Adam Schefter, seems to be a reflection of how the dynamics have changed since that time.

If a potential contract is closer to minimum levels, or structured in a way in which it is heavy with incentives, maybe it could be a fit for Bill Belichick's club. Or, at the least, the Patriots now have more motivation to explore if it could be a fit.

That seems like the best way to sum up Monday's meeting.

The Patriots will be adding to their running back corps between now and when they fill out their 90-man roster by late April/early May; that is a guarantee. No team goes into the offseason camps/training camp with just four running backs (James White, Dion Lewis, Rex Burkhead, D.J. Foster), and the Patriots' need for a power back is obvious.

The odds are highest that at least one addition is a rookie via the draft (or after the draft), but for a team that is always considering contingency plans and monitoring the fluctuating financial market with a wide variety of players, the Patriots are wise to at least go through the due diligence process with Peterson.