Sir Hoyle said that he wanted to see Parliament packed again by the end of the year but pledged not to “compromise health and safety”.
There are currently strict rules in force to prevent the spread of COVID-19, with the number of people allowed in the chambers limited to allow for social distancing.
Under the rules, a maximum of 50 MPs are allowed into the Commons chamber in person, while up to 120 can join debates remotely via the Zoom video conferencing app.
But the Prime Minister said he is eager to pack the Commons chamber with members during Prime Minister’s Questions, although those present will not be asked wear a mask.
Sir Lindsay said he and Commons Leader Jacob Rees-Mogg had lobbied for daily testing in a bid to pave the way for more participation in debates, adding that he had spoken to the NHS and government about getting a “quick turnaround of tests” to enable more MPs to enter into the chamber.
Sir Lindsay told the Times radio G&T programme on Sunday morning: "To be quite honest with you, I'd like to do it daily, not weekly. The problem is weekly testing doesn't tell you anything.
“I'll be quite honest with you, I've made approaches to the NHS and Government to say, look, why can't we have a testing system? What we would need is a quick turnaround of tests in order so that we can get MPs in.
"I personally would have had the heat screening equipment in to test temperatures.”
But he said Rees-Mogg had concurred that asking MPs to wear a mask while on the green benches “wouldn't work” as it would make recognition more difficult and be an obstacle to making speeches.
Tory MP Sir Desmond Swayne agreed, telling Yahoo News: “Happy to be tested, but not to be masked.”
A House of Commons spokesperson said: “The UK Parliament is a COVID-19 secure workplace, meeting all government guidance. This follows on-going work since the initial publication of the risk assessment on the 28th May.”
Sir Hoyle also said that the Prime Minister’s attack on Labour leader Sir Keir Starmer at Prime Minister's Questions this week had made him feel “uncomfortable”.
Johnson accused Sir Keir of being “a leader of the opposition who supported an IRA-condoning politician who wanted to get out of Nato”, apparently referring to Jeremy Corbyn.
“The chamber sets the tone, and that was not a good tone I wanted to see. To accuse somebody of basically being a supporter of the IRA, someone who had actually prosecuted the IRA, was touching a nerve of something I didn’t quite like,” he said.
Last week, former Cabinet minister David Davis criticised a government motion to continue virtual proceedings in the Commons until November, insisting full house is needed as key decisions on the COVID-19 response and Brexit are to be made.
Davis told the debate: “This is the weakest House of Commons I have ever seen. It does not do its job.
“The House of Commons at its best is far greater than the sum of its parts, it’s an organic entity that actually reflects our constituents’ interests and pushes the Government to do better, to govern better, to make the right decisions first time out not after several, er, preliminary attempts.