He said the situation was a “rollercoaster ride” as some MPs were withdrawing their letters to the backbench 1922 Committee in response to party whips.
A vote of no confidence can be triggered if 15 per cent of Conservative MPs – which would mean 54 currently – write to the chairman of the 1922 Committee.
Mr Ross said: “I think what we’ve seen over the last few days is more and more MPs publicly saying they take a similar position to me that regretfully they’ve reached this conclusion.
“And there’s a feeling that we’re getting closer and closer to the 54 number of letters required to go into the 1922 Committee
“Which suggests that there are far more than those of us who have publicly stated our position that are unhappy with the current Prime Minister and his position leading the Conservative Party.”
Mr Ross said only 1922 Committee chairman Sir Graham Brady knows exactly how many letters have been sent.
Asked how near the rebels are to the threshold, Mr Ross said: “I think it is near, but while members can submit letters they can also withdraw their letters.
“And I know there is a significant operation going on by the whips at the moment encouraging colleagues who may have submitted a letter to withdraw it again.
“So I do think we’re on a bit of a rollercoaster ride. It’s going up and down.
“But I think most people believe we are getting closer to the 54 number than further away.”
Asked why other Scottish Conservative MPs had not publicly supported his position, Mr Ross said they were “perfectly entitled to come to their own conclusion”.
He continued: “I think we’ve seen an awful lot of support for my position from MSP colleagues in Holyrood.
“I’ve spoken to council leaders, I’m speaking to members all the time.
“I’m not saying universally it’s 100 per cent behind me, because I understand people support the Prime Minister.
“They want him to get on with the job we were all elected to do just a couple of years ago.”
Earlier on Wednesday, Mr Johnson dodged a question about whether he agreed with Jacob Rees-Mogg the Scottish Conservative leader was a “lightweight”.
Mr Rees-Mogg’s comment was made in retaliation when Mr Ross called for Mr Johnson to resign after he admitted attending a drinks party at Downing Street during lockdown.
Mr Rees-Mogg, the Leader of the House of Commons, claimed Mr Ross was “not a big figure” in the Conservative Party and described him as a “lightweight” during television interviews.
During Prime Minister’s Questions on Wednesday, Labour MP Stephen Kinnock challenged Mr Johnson to say if he agreed with his Cabinet colleague’s remarks about Mr Ross.
Mr Johnson avoided mentioning Mr Ross and argued Conservatives in Scotland are doing “an excellent job”.