The Football Association says it is in talks with the BBC and BT Sport to show FA Cup games which had previously only been available on betting websites.
The FA has been criticised for its decision to sell FA Cup broadcast rights, via a third party, to seven gambling websites.
The seven betting companies have since said they "did not seek exclusivity".
They added that they would be "happy" for the games to be shown on a free platform elsewhere.
In a statement on Friday, an FA spokesperson said: "The FA is in discussions with the BBC and BT Sport, our UK broadcast partners for the FA Cup, to ensure that every FA Cup match scheduled outside of the Saturday blocked broadcast hours is now made available to watch live on BBC, BT Sport or on FA platforms. Further details will be confirmed in due course."
It is understood the FA would not want matches shown to clash with other television broadcasts of live matches. There was a match broadcast in each of the kick-off slots during the FA Cup third round last weekend, except for the 15:01 GMT start time.
Last weekend, ties started one minute late as part of the 'Heads Up' mental health awareness campaign.
The seven gambling websites - Bet365, Betfair, William Hill, Coral, Ladbrokes, Unibet and Paddy Power - acquired the rights via agency IMG, who agreed a deal with the FA.
In the third round of the tournament, 23 matches were available to watch on Bet365 last weekend - all those that did not kick off at 15:01 GMT on Saturday.
The matches were available to anyone who has placed a bet or put a deposit in their account in the 24 hours before kick-off.
In July 2017, the FA announced it was cutting its ties with gambling firms, but the deal with IMG was made in January 2017.
The government is "very angry" about the issue and Sports Minister Nigel Adams has said he will meet the FA next week.
On Thursday, Brigid Simmonds, chairman of the Betting and Gaming Council, said: "Our members did not seek exclusivity for the rights to screen FA Cup games.
"They are therefore happy for IMG to offer the rights to screen these games to the Football Association or another appropriate body so that the games can be viewed for free by the public with immediate effect."
The FA has said it will "review this element of the media rights sales process ahead of tendering rights from the 2024-25 season," but the government want it to look at taking action earlier.
BBC sports editor Dan Roan
The FA now have two weeks before the FA Cup fourth round to reach an agreement with rights holders BBC and BT that enables them to show matches that would have been streamed exclusively by bookmakers, until the betting companies agreed to relinquish them.
Amid a barrage of criticism from politicians and anti-gambling campaigners, the FA believes negotiations are progressing well and a solution is now in sight over a deal that was signed in 2017, before it started to distance itself from the betting industry.
However this has been an embarrassing episode for the governing body. It has reinforced concerns that via extensive sponsorship of clubs, stadia and even competitions, along with advertising at matches and across match coverage, football is being used to normalise betting.
And there will be many who now feel that this controversy strengthens the case for the kind of regulation that Italy has introduced, where clubs are barred from having gambling sponsors.