DALLAS — The Yankees and Mets both remain heavily involved in the five-team Juan Soto Derby, with both clubs recently upping offers into the $710 million-$730 million range — MLB record territory — as it’s believed the sweepstakes could be within a day or two of an historic conclusion.

Both New York teams showed how serious they are with recent changes to offers, and both now have extended bids above Shohei Ohtani’s record $700 million deal.

It is believed the Mets may be slightly higher as of Saturday night, but the respective offers appear to be within shouting distance.

Juan Soto is set to sign a potentially historic contract.Jason Szenes / New York Post

There is no word yet that any of the other three Soto suitors — Red Sox, Blue Jays and Dodgers — are by any means out of this bidding, and it’s possible one of those teams might even be above the New York teams and win the 26-year-old superstar hitter.

Soto won’t necessarily take the exact highest bidder, and he was said to be weighing five enormous bids Saturday night.

At least the top-four offers are believed to be fairly close.

The Mets understood from the beginning that the Yankees’ one untouchable advantage in this sweepstakes is their ability to offer a two-time MVP winner, Aaron Judge, as lineup protection.

Some new school folks scoff at the idea of protection within a batting order, but Judge was the American Leader OPS leader with a 1.159 mark, so far above everyone else that Soto didn’t lead the league in walks for a rare time.

Judge did with 133 free passes to 129 for Soto.

Aaron Judge thrived with Juan Soto last season.JASON SZENES FOR THE NEW YORK POST

The Mets are also seen as an attractive destination for Soto, as his meeting with Mets higher-ups, including club owner Steve Cohen and team president David Stearns, was said to have gone well (as did the Yankees’ meeting a few days later).

The Mets impressed Soto with their stunning run to reach the NLCS last year in Stearns’ first season at the helm.

The Red Sox and Blue Jays are also believed to have placed very competitive bids, while the superteam Dodgers, with less need to add yet another superstar, surprised folks just by going well over $600 million.

All three of those teams seem to still be in the bidding, though the lowest-bidding Dodgers are still viewed as the least likely destination despite their obvious attractiveness.

Steve Cohen and David Stearns during the NLCS in Los Angeles.Charles Wenzelberg / New York Post

Soto met with higher-ups of all five teams last month, even including the Yankees — although Soto was said to have grown progressively more comfortable in the Yankees’ environment over the year he was in The Bronx.

He is thought to have made a connection with Judge on that level, too.

Judge also made things easy when he said that he hoped Soto could get whatever he could in the market, even if it meant it was more than him.

If Soto signs for exactly $720 million, coincidentally, it will be exactly double Judge’s then-free agent record $360 million deal — set only two years ago.

Soto was projected to break Ohtani’s present-day value record of around $450 million, but nobody predicted him to beat Ohtani’s mark by 60 percent, which will be the case if no money is deferred in his deal.

Ohtani’s contract called for 97 percent in deferrals, so $680 million of the $700 million will be paid later.