It is believed the club would like to keep the 34-year-old around beyond the end of his current deal, which expires this month.
And if he does opt to stay, he would continue to serve as a back-up keeper at Molineux.
Ruddy has been a very popular and important member of the dressing room throughout his four years with the club, although he has struggled for regular game time in recent seasons.
He signed a one-year extension last summer and the offer is thought to be of a similar nature this time around.
There is the feeling, though, that the former Norwich man might choose to look for a first-choice opportunity elsewhere rather than stay under Wolves’ new regime – former Benfica manager Bruno Lage set to be confirmed as their new boss soon.
Ruddy, in total, has played 66 times since joining Wolves in the summer of 2017, and 45 of those games came in his first season.
The shot-stopper, who was capped once by England in 2012, kept a whopping 24 clean sheets to earn the Championship’s Golden Glove award as Nuno Espirito Santo’s side won the title.
Since the arrival of Rui Patricio upon promotion to the Premier League, though, he has mainly just been used in the cup competitions.
He played all the way through as Wolves reached the semi-finals of the FA Cup in 2018/19.
The past two seasons have seen him make 12 appearances in all competitions, while he has also featured for the Wolves Under-21s as an overage player in the Football League Trophy.
First-choice shot-stopper Patricio continues to be linked with a move to Italian club Roma.
Reports in the country claim Patricio’s agent Jorge Mendes has offered the 33-year-old to Jose Mourinho’s side ‘for some time’, although PSG’s Alphonse Areola – who spent last season on loan at Fulham – is also an option.
Patricio is entering the final year of his current deal at Molineux and will feature for Portugal in the upcoming Euros.
Wolves eventually paid £16million for him in October 2018 after he terminated his contract at Sporting Lisbon.
Meanwhile, Portuguese midfielder Vitinha has admitted he expected more playing time while on loan at Wolves last season.
The young playmaker featured more in the final stages of the campaign, making five league starts in the end.
Wolves, and the incoming Lage, still have to decide whether to sign him on a permanent basis from Porto.
The same applies to Rayan Ait-Nouri while a permanent deal for Willian Jose appears unlikely to be pursued.
“I’m not going to lie, I came with the idea of having more minutes, playing more and being in the team more often, but it didn’t happen,” said Vitinha.
“I had the same type of opportunities and tried to make the most of every bit of it to show my value and help the team.
“Of course a player always thinks it can be better and I will aim for that.
“I was surprised (when Wolves signed me) but at the same time very happy, because Wolverhampton is a good club and this is a great league. That is why I accepted it.”