Whether or not the Rays have a realistic shot of winning their division (they currently sit in last place, eight games back of Baltmore) seems to be beside the point, or at least that is the image they are attempting to project. Joel Sherman is putting out the idea that Tampa may not be as eager to move on from Price as everyone else seems to think they should be:
Six weeks ago this was a no-brainer. The Rays were 18 games under .500 on June 10, 15 games out of first and they were the majors’ lone club with a sub-.400 winning percentage (.364). Injury and underperformance had left perhaps the smallest of small-market teams in obvious sell mode.
But a funny thing happened on the way to July 31: The Rays have gone 23-11 since (through Sunday), which put them between the Angels (23-10) and A’s (22-11) for the best record in that time frame. Tampa cut its AL East deficit exactly in half to 7 ¹/₂ games. And many of the key Rays (including Price) remain from the club that erased a nine-game deficit on Sept. 1 to overtake the Red Sox for the 2011 AL wild card.
Putting aside the differences between the 2011 Rays and their current incarnation, what you are essentially asking for is lightning to strike twice in order to get the Rays to the postseason this year. While the odds aren't exactly zero, it would be a curious decision to hang on to David Price for five more months - only to lose value in an off-season trade - for what is a considered to be an exceptionally long shot to even play in the postseason.
Could it happen? Sure. Will it happen? Most likely not. One Wild Card team will come from the AL West, and possibly a second if Seattle can keep it up. After Seattle, Tampa would have to leapfrog the Yankees, Blue Jays, Indians, Royals, White Sox, and Red Sox. That's a lot to hope for.
If the Rays want maximum value for Price, now is the time. It sounds like they are going to hold onto him for at least another week, unless Seattle comes calling with Taijuan Walker, James Paxton, et al. But if they decide to hang onto him past July 31, it would be a mistake, regardless of what happens the rest of this season.