The president also sent a tweet on Friday that explicitly stated he was aware that he is under investigation.
"There's been no noification from the special counsel's office there is an investigation" of him, Sekulow said.
The attorney told both shows - as well as the NBC News and Fox News Sunday morning programs - that Trump was simply responding to a Washington Postreport that said special counsel Robert Mueller's Federal Bureau of Investigation probe has widened to include a look into potential obstruction of justice and financial crimes by Trump associates.
Barak Cohen, a former Justice Department lawyer and now a defence attorney specializing in white-collar crime and investigations, said there was no requirement that the special counsel notify Trump he was under investigation, so the lack of such notice meant nothing.
"The tweet from the president was in response to the five anonymous sources purportedly leaking info to the Washington Post", he said.
"You're right, Chris. I can not read the mind of the special prosecutor", Sekulow responded. "The best thing that could happen for the president, and the country, is a full and credible investigation".
During an interview on CNN's "State of the Union" Sekulow explained to Jake Tapper that Trump wasn't able to clarify that he was referring to the WashingtonPostreports in his tweets because of the "limitation" Twitter has on characters used in a tweet.
And it kept going on and on like this until finally Wallace figuratively threw his hands in the air, responding to Sekulow saying there's no investigation after saying he didn't know if there was one. "He's not afraid of the investigation - there is no investigation", Sekulow told NBC channel. He said he had only been discussing the constitutional problem posed if the president were being investigated.
A USA official who is familiar with the rough outlines of the probe and who spoke on condition of anonymity told Reuters on Thursday that Mueller was also examining whether Trump or others tried to interfere with the investigation.
Trump's statements on Twitter are a sign of his frustration with the Russian Federation allegations, said former Republican Speaker Newt Gingrich, on ABC's "This Week".
During testimony before the Senate Intelligence Committee on June 8, Comey testified that he felt pressured by Trump to drop an investigation into the president's top national security adviser Michael Flynn's links with Russian Federation.
Rep. Adam Schiff of California, the ranking Democrat on the House Intelligence Committee, accused Trump of attempting to take down Mueller just as his investigation is getting underway. They're essentially engaging in a scorched earth litigation strategy that is beginning with trying to discredit the prosecutor. "I don't think that tweet helped him".