Wrexham co-owner Reynolds criticised the National League on Monday for its "truly baffling" failure to consider allowing clubs to stream live matches domestically and internationally.
Reynolds accused League officials of neglecting to pursue a plan to open talks with BT, who currently own the rights to the competition in the UK, about potential streaming.
"After months of maximum effort, the decision (through inaction of the Vanarama National League) to not allow domestic/international streaming of matches of Wrexham and the other clubs in the league is truly baffling," Reynolds wrote to his 20 million Twitter followers.
"Depriving every team in our league the chance to expand the fanbase while adding to league revenue benefits everyone. This is a spotlight and a chance and we ask the Vanarama National League to take it."
Reynolds tagged in all 24 National League clubs in his tweets - and on Tuesday sponsors Vanarama tweeted: "We are in favour of live streaming as long as it benefits all clubs in the league and is what the fans want.
"As the National League's title sponsor, we will talk to the Vanarama National League and BT Sport to make sure our voice is heard.
"And thank you to Ryan Reynolds for unblocking us. Glad we can come together on this and bring the National League to new levels."
Vanarama chief executive Andrew Alderson added: "We're in full support of Ryan Reynolds requesting more effort from the National League to televise all clubs.
"Vanarama, too, want what is best for the fans and pledge to work with him to bring the National League to new levels with more matches streamed, as long as it is what both the clubs and the fans want.
"We're in talks with all clubs to assess whether the broadcasting would be of benefit."
The Daily Mirror reported a spokesperson from the National League as saying: "There are wider discussions about streaming for all clubs that are subject to ongoing contracts and we are working with partners to deliver the best solution for all."