BOSTON -

The rumbling is getting louder.

With Boston out of contention in the American League East and the non-waiver trade deadline set for 4 p.m. ET on Thursday, the Red Sox are taking calls about potential trades for Jon Lester, with the likelihood increasing that the ace left-hander could be dealt this week.

It makes sense. Under owner John Henry, the Red Sox have been averse to signing over-30 pitchers to free agent contracts in excess of four years. And with Lester having the best season of his career, he figures to be seeking a contract in line with the six-year, $144 million deal that left-hander Cole Hamels signed with the Phillies in 2012.

Thus, the price for Lester might be far more than the Sox are willing to pay. In addition, Henry told the Boston Herald last week that the Red Sox agreed to suspend negotiations with Lester until after the season.

It is believed the Red Sox told teams they would need at least two elite-level prospects in any deal for Lester. The Los Angeles Dodgers might still be the front-runner, and they could offer a package fronted by touted center fielder Joc Pederson. The St. Louis Cardinals could move either of their outfield prospects, Oscar Taveras or Randal Grichuk.

Seven National League teams (the Washington Nationals, Atlanta Braves, Milwaukee Brewers, Pittsburgh Pirates, Cardinals, Dodgers and San Francisco Giants) are within two games of their division lead. Lester, who allowed a total of six runs (three earned) in his past five starts, seemingly could help push any over the top.

Various reports indicated the Seattle Mariners and Baltimore Orioles expressed interest in Lester.

Any deal involving Lester isn't likely to be completed until late Wednesday or Thursday. Lester is scheduled to start Wednesday night's series finale against the Blue Jays at Fenway Park. Toronto won the series opener 14-1 Monday.