Trump also said in his tweet midday Saturday that he "fired" Flynn "because he lied to the president and the FBI."
Flynn, a retired lieutenant general, was forced to resign as Trump's national security adviser in February after only a few weeks on the job following the revelation he misled Vice President Mike Pence and other administration officials about his meeting with the Russian ambassador, Sergey Kislyak, during the transition period between Trump's election and his taking office.
Nothing was said publicly at the time by administration officials about Flynn's also lying to the FBI.
On Friday, however, the retired lieutenant general pleaded guilty to one count of lying to the FBI about his back-channel negotiations with the Russian ambassador during the transition period. The former Trump aide has promised "full cooperation" in the special counsel's Russia investigation.
Flynn initially denied that he discussed U.S. sanctions placed on Russia with Kislyak, but transcripts of Flynn and Kislyak’s phone calls reviewed by Justice Department lawyers showed otherwise.
Trump's tweet about Flynn on Saturday followed earlier comments he made to the press about his former aide.
The president was on Saturday morning heading away from the White House to travel to New York City for a day of fundraising events when a reporter asked if he is concerned about what Flynn may tell Special Counsel Robert Mueller.
"No, I'm not," Trump said. "What has been shown is no collusion, no collusion. There has been absolutely no collusion."
"So we're very happy and, frankly, last night was one of the big nights," he added, possibly referring to the Senate's overnight passage of the massive GOP tax overhaul.
Asked if he still stands behind Flynn, Trump said: "We'll see what happens."