The pair are showing more and more interest in broadcasting live sport, with Facebook attempting to secure the digital rights of the Indian Premier Leagu (IPL) earlier this month.
They failed in that quest but Amazon successfullly secured a deal to broadcast 10 Thursday night NFL games this season for a fee of £37m soon after beating Sky to the rights to the ATP tennis tour.
Woodward believes that it is only a matter of time until the two tech firms set their sights on the Premier League.
"Absolutely, I think they will enter the mix; anecdotally, there was incredibly strong interest in the last cycle," he explained.
"We are hearing that around the Premier League table, and we are also hearing that from a European perspective in terms of interest in the Champions League and Europa rights. I do think we are going to see an increasing engagement from these, and we would welcome the interest.”
The Premier League are thought to be preparing tender documents to send out shortly for their next rights cycle (2019-2022).
The current domestic and overseas Premier League TV rights deals are worth a combined total of £8.3bn.
Could we be set to watch Premier League football on Facebook in as little as two years' time?