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 $700M deal. It is believed the Mets may be slightly higher as of Saturday night, but the respective offers appear to be within shouting distance.

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 may 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 fairly close.

The Mets understood from the beginning that the Yankees’ one untouchable advantage in this derby 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 League OPS leader by 10 percent 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.

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 $600M.

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.

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 announced that he hopes Soto gets whatever he can in the market, even if it means it’s more than him.

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

Soto was projected to break Ohtani’s present-day value record of around $450 million, but nobody predicted he’d 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.