Rumors have increased significantly with a month left before the non-waiver trade deadline (Aug. 1). Contenders are exploring ways to upgrade their roster and have scouts doing their homework in case teams, like the Yankees, decide to be sellers.

The Yankees have not waived the white flag on the season yet. Many within the game think Brian Cashman should trade players like Andrew Miller and Aroldis Chapman and acquire players that will put them back in race next season and beyond.

If the Yankees decide to trade Miller or Chapman, the two southpaws will impact the pennant race so teams will line up with their best offers to acquire the dominating lefty relievers.

The Cubs, Nationals, Giants, Dodgers, Red Sox and Rangers are believed to be among the teams that will make a run at either Miller or Chapman.

The Yankees are expected to receive significant packages in return for Miller and Chapman due to supply and demand. And the fact Cashman will be able to have teams bid against one another and run up the price.

Buster Olney reported Wednesday that rival executives expect the Yankees to “set a high price on Miller.” The Yankees do not have to trade him. Miller is under contract for two more seasons beyond this one. But teams think Cashman will “take advantage of his very high trade value in the market right now.” The Yankees are expected to ask “for specific prospects from other teams and tell them they can either meet the demands or they won’t get the player.”

Olney spoke with “one evaluator with knowledge of the Yankees’ interest” and that person believes Cashman “will tell the Cubs that if they want Miller, they will have to part with young hitter Kyle Schwarber.” And if the Cubs say no to Schwarber, “the Yankees can simply move on to conversations with other contenders who are interested in the left-hander.”

The Yankees are in a position, as Olney explained, to set the market for Miller and if teams are not willing to pay the price to acquire him, then he will be part of the Yankees pen at least for the rest of this season.

Buster Olney reported the asking price for Chapman will be less than Miller because he’s a free agent at the end of the season.

The Cubs have had scouts watch Andrew Miller and Aroldis Chapman at least twice in the last three weeks. Theo Epstein has ties to Miller. Epstein traded for Miller when he was the GM of the Red Sox. And not only were the Cubs linked to Miller before he signed with the Yankees, but rumors last winter pointed to Epstein talking to Cashman about him.

The Cubs are looking at ways to upgrade the backend of the bullpen and give Joe Maddon dependable options for late in games. Whether or not Theo Epstein and Jed Hoyer will pay the price to acquire Andrew Miller is unknown at this point. But if the deal has to include Kyle Schwarber, those conversations will end quickly. Schwarber is one of a handful of players that is believed to be untouchable.

• Report from Buster Olney

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