The Olympic swimmer has previously admitted that he would be interested in starring in the ABC dating show, while host Chris Harrison has said he'd be "great" in the role.
However, a source has now told E! Online that while Lochte has been "approached" and the athlete is "open" to the idea of starring on the show, he is "not the top choice".
"It's really a three-way tie," the insider added, referring to Lochte and recent Bachelorette contestants Arie Luydendyk Jr and Sean Lowe. "My guess is it won't be Lochte, but it keeps changing."
Meanwhile, Lochte's manager Erika Wright denied rumours that the gold medallist is asking for $750,000 (£475,000) to appear on The Bachelor.
"We have only had preliminary contact with The Bachelor," she said. "Absolutely no figures have been discussed and no-one from Ryan's team has made any comment with regard to compensation."
Wright also insisted that Lochte's "top priority" is training for the Rio Olympics in 2016, although the source revealed that he has been approached for a number of television projects, including NBC's upcoming dating series Ready for Love.
"Ryan is keeping all of his options open," Wright said. "He is very fortunate to be in this position and is taking every offer with great consideration."
Lochte recently filmed a guest role for the upcoming new season of 90210.