The Saints chief said televised matches would "show that we're fighting back" against the virus, but he's unlikely to receive much support for the idea.
The English top flight is currently suspended until at least 30 April, with the season not expected to resume until many weeks after that date.
Semmens told BBC Radio Solent he feels that the nation would benefit from Premier League games being played and televised daily, given that people are spending an increased amount of time in their homes.
"We have to do what is right and safe for the general public," Semmens said.
"When everybody is safe and we're not using up NHS and police resources, the government would like us to get back to playing because we are entertainment and a sign that the country is coming back to normal.
"If people are home for another month and Premier League football is on the TV every day that can only be a good thing. Not because we are more essential than the NHS but because we can give people entertainment and show that we're fighting back."
With some estimates on when the 2019-2020 season might eventually be completed reaching beyond June, Semmens highlighted the "legal challenges" that clubs and competitions might face.
Many players' contracts expire on 30 June, and Semmens said: "We hope to get the league done by the end of June. As soon as you go past that date, there are legal challenges.
"If we ended up playing until 15 July and you had to extend a player's contract by two weeks, convincing a player to play two more weeks of football and get paid nicely to do it — I don't believe that will be a substantial challenge.
"The challenge is making sure we don't have a knock-on effect to other seasons and make football compromised for years to come."