Saquon Barkley’s contract offer from the Giants has been increased. The Giants improved the guaranteed part to just north of $22 million, according to reports from Giants Insider and NorthJersey.com, after Barkley had rejected a multi-year agreement at $13 million per year with only $19.5 million guaranteed, as was first reported last week by The Post.

However, sources informed The Post that the Giants reduced the average annual value of their most recent offer in return for raising the guarantees. The $22 million is significant because it is close to the amount Barkley would be guaranteed ($22.2 million) if he were to play in 2023 and 2024 under the franchise tag.

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Since there had been no communication for weeks prior to Monday’s 4 p.m. deadline for reaching an extension, it is positive for the Giants that the parties are at least exchanging bids and talking on Monday.

Once that time has passed, Barkley will either have to play under the franchise tag (a one-year, $10.1 million contract) or sit out of the game, either for training camp or the entire regular season, which would result in his losing out on weekly wages.

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A running back needs guaranteed income more than anyone else because of the position’s limited shelf life and the amount of wear and tear that might be expected.

Christian McCaffrey (49ers), Alvin Kamara (Saints), and Derrick Henry (Titans) all have contracts with guarantees of more than $22 million, and free agents Dalvin Cook and Ezekiel Elliott have contracts with guarantees of more than that amount from prior contracts with the Vikings and Cowboys, respectively.

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Including the playoffs, Barkley, 26, had a career-high 377 offensive touches and 1,312 rushing yards in the regular season. He has been open about wanting to play his entire career in New York and secure a seat in the team’s Ring of Honor. He made $38.6 million in his first five seasons with the Giants.