Rigell's spokeswoman, Kaylin Minton, confirmed the Times's report but declined further comment.
The congressman said in March that he would not vote for Trump.
"I believe that Republican voters have got a reason to be upset and angry, but I'm submitting to them that the solution is not Donald Trump in any respect," he told CNN at the time.
Johnson, the former governor of New Mexico, also has the support of former representative Tom Campbell, a Republican from California, according to his website.
Rigell, a former car salesman, has bucked the GOP establishment in the past and worked with Democrats to ban straw purchases of guns, to oppose stopgap funding measures and to challenge President Obama's actions in Syria.
Forty percent of primary voters in his Virginia Beach district favored Trump in the primary, and the region, home to a high percentage of servicemen and women and retired military personnel, is key to Trump's Virginia strategy.
State Del. Scott Taylor (R-Virginia Beach), a former Navy SEAL, defeated Rep. J. Randy Forbes in the June Republican primary, and he is the favorite to win the general election in the Republican-leaning district.
Rigell backed Forbes, who switched districts after a court-imposed elections map added Democrats to Forbes's district.
Taylor has capitalized on the same national hunger for an insurgent candidate that has helped propel Trump, and adopted a similar slogan: "Let's all make American great again."