Speaking at Royal Birkdale, where she will be competing in the Ricoh Women's British Open this week, Matthew said it was "great" that the club's 2500 members are finally being given the chance to open their doors to women after 260 years as a single-sex club.
"I think the R&A should remember it governs the world of golf everywhere, apart from the US and Canada [and Mexico]," said Matthew, who won the British Women's Open at Lytham in 2009. "I think they should have lady members and hopefully they will vote that way in September."
When Augusta National, hosts of the US Masters, ended its men-only policy in 2012, the former US Secretary of State Condoleezza Rice was one of the first two women to be offered memberships, and Matthew admitted that she would relish the same invitation from the R&A if, as expected, its members follow their general committee's advice and vote to be an open club. "I'd be delighted," she smiled. "I'd be very honoured."
Currently No.15 in the world, Matthew is the highest ranked British player in the Royal Birkdale field, and she showed impressive form in last month's US Women's Open at Pinehurst, where she finished in a tie for 10th place. She has also finished third in two LPGA Tour events this year.
"I'm pleased with how I'm paying," she said. "I've played well all year. The weeks I've been up there have been the weeks I've putted a bit better. This week, I'm going to have to drive it well and keep it on the fairways, but at the end of the day it always comes down to who holes the most putts.
"I think this course is definitely playing longer than it has in the past. You're definitely not getting as much roll on the fairways. There are some tough holes out there and the fairways are pretty tight. You're going to have to play really well to have a good score round here, especially if the wind blows."
As mother to seven-year-old Katie and five-year-old Sophie - she was born just 11 weeks before Matthew won the event in 2009 - the North Berwick native has to work hard to achieve a sensible work/life balance, but her husband (and former caddie) Graeme now has primary responsibility for looking after the home, allowing Matthew at least a little more freedom to pursue her sporting dreams.
"Obviously, it is very busy," she explained. "Even when I am at home I probably don't practise as much as most people. Our youngest starts school in August, so I'll have from 9am to 3pm to squeeze everything in, whereas, for the past few years, it has been from 9am to 1pm. You just have to make your practice higher quality. You get around it.
"I couldn't have done it without Graeme's help over the years. He's been very supportive and now he's at home looking after the children more, which he is finding is harder work than caddying. He often said he would quit caddying for me, but I think he'd rather come back caddying now. But, obviously, you need great support from your family if you're going to do well, so I've been lucky."
Stacy Lewis, the reigning champion and current world No.1, has predicted that Michelle Wie will become a dominant force in the game after breaking her major title duck at the US Open, and that everyone will benefit from her success.
"Seeing her playing good golf is good for the other players," said Lewis. "The US Open couldn't have been scripted any better. She is our biggest star and she moves the needle. Her winning there was huge for us."