The injury caused him to miss the Milwaukee Brewers' 2008 postseason.
Major league officials told MLB.com Thursday that Brewers assistant general manager and Sheets' agent have had discussions this week about who would pay for the procedure.
"We're working our way through all of the details and we don't know the answer yet," Brewers Assistant General Manager Gord Ash told the Web site. "Major league baseball has regulations related to workers comp and there are procedures and protocols that have to be respected."
Late last week, Sheets, a free agent, agreed a two-year contract, pending a Rangers' team physical.
"We've maintained contact but I'm not optimistic at this point," Rangers' General Manager Jon Daniels said Thursday.
Last season, he went 13-9 in 31 starts with a 3.09 earned run average but Milwaukee declined salary arbitration for 2009.