Nathan would become the most attractive closer if made available, according to Rosenthal. The Boston Red Sox, Detroit Tigers and Los Angeles Dodgers are all looking too add a reliever before the trade deadline.
Texas has attempted to add offense, but have been unable to work a deal. The Rangers have lost 11 of their last 14 games and rank ninth in the AL in runs scored.
Nathan has pitched well for the Rangers this season, sporting a 1.73 ERA while saving 32 games in 34 opportunities. The closer is owed around $2.5 million for the rest of the season, with a potential club option for $9 million in 2014. Nathan has finished 39 games this season and could void the club option if he finishes 55 games.
Texas believes that they have the depth to replace Nathan. Joakim Soria could slide into the closer's role; he closed 160 games in five seasons for the Kansas City Royals. Former Rangers closer Neftali Feliz is expected to return from Tommy John surgery in about a month.