The gifted stand-off, 26, is suddenly available after he was surprisingly released with immediate effect by Canberra Raiders - less than halfway through his three-year contract at the NRL club.
Williams - expected to be a big part of England’s World Cup bid at the end of the year - wants to return to home due to personal reasons and with his partner Charlotte expecting their first child in a few months’ time.
Hometown Wigan Warriors have first option to speak to him as part of the conditions agreed when they sold the Great Britain international to Raiders while Warrington Wolves and Leeds Rhinos are also understood to be keen.
However, whether any Super League club can afford Williams immediately with regard to cap space remains to be seen.
With that in mind, ambitious Championship club Newcastle Thunder have made an audacious bid to recruit him and offered a short-term deal to his England-based manager Andy Clarke.
However, Chester says Wakefield - who picked up their first win of the season on Sunday - do have space in their cap if Williams was interested.
“We’ve certainly got salary cap space, let’s put it that way!” he said, when asked if Trinity had space for the brilliant half-back.
“Budget wise, we don’t know about that. But we have the cap space.
“He’s a fantastic player. I messaged his agent yesterday with a cheeky little text telling him to bear us in mind should anything arise.
“I’m really pleased he’s coming back to Super League.
“I never like to see our own go over to Australia and it’s important we keep all our best players in this competition.
“I’m looking forward to seeing him come back if and when that is.”
Chester admitted there were some laughing emojis in the agent’s response but added: “I do get on well with his agent.
“There will be a lot of clubs that are after his signature but there’s not many clubs that will have that salary cap space like we do.”
Jokingly asked if that was him saying Wakefield are in pole position, Chester replied: “That’s me saying we have a very, very small chance!
“But we do have the space and a fair amount of budget to go at.”