Don’t hold your breath for Rep. Michael McCaul (R) to jump into the open-seat Senate race in Texas.

The Texas Tribune reported Tuesday that McCaul was looking at joining the crowded GOP field seeking retiring Sen. Kay Bailey Hutchison’s (R) seat. The report said the very wealthy Congressman would be willing to spend $4 million to $6 million of his own fortune on the race. But a Republican source close to McCaul told Roll Call that he is not planning a bid anytime soon.

“He has taken no concrete steps towards a campaign for U.S. Senate,” the source said. “To my knowledge, he is not planning to take any steps towards a campaign for U.S. Senate.”

McCaul is well-regarded in the Texas delegation, but he would have a tough fight to win the GOP’s Senate nomination. The last two House Members to ascend directly to the Senate were Lyndon B. Johnson in 1948 and Phil Gramm in 1984.

Either way, the GOP Senate field is already packed. After Lt. Gov. David Dewhurst announced his campaign last month, he instantly became the frontrunner because of his high name recognition and great personal wealth. Former Texas Solicitor General Ted Cruz, former Dallas Mayor Tom Leppert and Railroad Commissioner Elizabeth Ames Jones are also seeking the Republican nomination.

McCaul could compete financially with Dewhurst’s largess. Last week, Roll Call declared him the richest Member of Congress with a net fortune of at least $294 million.

But two Texas Republican operatives cautioned that McCaul was not planning to run for Senate if Dewhurst jumped into the race.

Nonetheless, McCaul’s office did not deny reports that he’s thinking about running. He said in a statement that his “goal remains to ensure that the most qualified person represents Texas in the United States Senate.”

McCaul toyed with running statewide before. In the previous cycle, the GOP Congressman seriously considered running for Texas attorney general but eventually declined a bid.

Lone Star State Republicans say McCaul, a former federal prosecutor, is still eyeing the attorney general’s office. They argue that it’s no coincidence McCaul’s primary competition for that seat in several years might be Cruz, provided he doesn’t win the Senate seat.

Cruz’s Senate campaign has picked up momentum in recent weeks with several key endorsements, including from the Club for Growth and Sen. Rand Paul (R-Ky.).

Retired Lt. Gen. Ricardo Sanchez is seeking the Democratic nomination for the Senate seat.