Wednesday saw England and Wales Cricket Board (ECB) chief executive Tom Harrison announce he was taking a 25 percent pay cut, with other officials at Lord's reducing their salaries as well.
That followed his announcement on Tuesday of the ECB's £61 million aid package in response to the "once in a generation" challenge of Covid-19.
Harrison said on Tuesday there were no plans to enforce a pay cut on leading England players, with cricket worldwide suspended.
But the ESPNcricinfo website reported Harrison had written to the chief executive of England's Professional Cricketers Association' (PCA) to suggest centrally contracted stars such as Test captain Joe Root and all-rounder Ben Stokes volunteer to accept a cut of some 20 percent.
The players, however, do not yet appear to have been contacted directly.
"It's a tricky one, talking about finances and people's wages, it can be a delicate subject," World Cup-winner Woakes told BBC Radio.
"The PCA is our governing body (union) as players and they do a fantastic job for us. They're looking after us as well as they can and trying to help the ECB through this."
The 31-year-old Warwickshire star added: "Those discussions are ongoing between the ECB and the PCA and there's every chance that might happen but at the minute we haven't been asked to take a pay cut."
"By no means does that mean it won't happen in the future; we are likely to have to help the game get through this tough period. Time will tell."
The start of the English domestic season has been delayed until at least 28 May and doubts remain over the future of lucrative incoming tours by the West Indies, Pakistan and Australia.
Questions over whether well-paid sportsmen should accept pay cuts became a political football on Thursday when the British government said Premier League soccer players - who earn considerably more than their cricket counterparts - should take a pay cut, amid outrage at top-flight clubs using a government furlough scheme for non-playing staff.
Health Secretary Matt Hancock said "everyone needs to play their part" in the coronavirus fight-back, adding: "That means Premier League footballers too... take a pay cut and play their part."
But players across all sports have also been involved in fundraising initiatives, with Jos Buttler, an England team-mate of Woakes, auctioning the shirt he wore in last year's World Cup final win on behalf of two London hospitals.
"It's an incredible thing Jos has done, to give away one of his most valuable shirts," said Woakes.
"The price is already up at £65 000 upwards. Let's hope it can get up to £100 000."