BBC Scotland is understood to be offering the league 拢16m for the rights to broadcast matches on radio and TV in Scotland over two years.
Channel 5 is offering a deal that would see games screened in homes right across the UK.
A Channel 5 executive, who was quoted in Scottish newspaper Business AM, said: "Football has traditionally done well for us in the past and we have shown a few Scottish internationals which proved very successful. There is certainly a wider audience than just Scotland."
The deal had been expected to be finalised on Friday after 10 football teams voted in favour of the BBC's offer, but the deadline was extended after Rangers and Celtic, known as "the old firm", failed to cast a vote.
Channel 5 believes the matches would bring real value to the station. It has the funding to pay for the rights after its programming budget was raised earlier in the year.
"We have certainly got the funds available to us, and it is felt that Scottish football would bring real value to the station. It is an exciting property for us. But it is all in the hands of Scottish Premier League," the Channel 5 source said.
Channel 5 still has to win the support of the football clubs, which it seems unlikely to get. The league is holding an extraordinary meeting today to decide who to award the contract to.
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