MLB was still trying Monday to sort out what had happened a day earlier in Chicago.
Price accused Hallion of directing an expletive toward him during the Rays' 8-3 win over the White Sox on Sunday. The AL Cy Young winner thought Hallion missed a pitch and exchanged words with the plate umpire while heading to the dugout after the seventh inning.
Hallion later called Price a "liar." Price took to Twitter and disputed Hallion's version.
The Tampa Bay Times reported MLB vice president Joe Torre and other officials are reviewing the matter. Hallion could face discipline for initiating the incident and for the language he allegedly used, the newspaper reported. Generally, discipline against umpires is not announced.
Price and teammates Jeremy Hellickson and Matt Moore could face discipline for violating MLB's social media policy, which prohibits "content that questions the impartiality of or otherwise denigrates a Major League umpire," the newspaper noted.
Information from The Associated Press was used in this report.