Alfie Hewett and Gordon Reid are aiming to complete the set by winning Paralympic gold this summer.
The British pair are a dominant force in wheelchair tennis, having won 19 grand slam doubles titles together.
But they have never won gold at the Paralympics, taking silver in Tokyo three years ago, and want to put that right in Paris later this year.
“It is a big target of ours, we want to achieve our goals there,” Reid told the PA news agency.
“It’s a special challenge and honour to represent your country and be part of that team which once every four years is something you want to take with both hands.
“The slams are big for us but the Paralympics are for us as well.”
It is a big year for Hewett as he tries to double up by winning a first Wimbledon singles title and a Paralympic gold.
The 26-year-old has eight grand slam singles titles but his home one has so far evaded him, finishing runner-up in the last two years.
Asked which he would want more, a Wimbledon singles title or a Paralympic gold medal, he said: “I couldn’t pick between the two, they both mean a lot.
“Obviously Wimbledon is first so I will be concentrating on that and hoping I can join G in the winners’ circle.
“But they are both special events and you can’t rank them. They are very unique in their own way.”
If Hewett could get to another Wimbledon final he would love the chance to play on Centre Court.
The wheelchair tennis finals were played on Court One last year, but Hewett says it would be a great message if it was upgraded.
“I wouldn’t turn it down, it would be huge for disability sport to have a match like that at Centre Court in one of the biggest events of the year,” he added.
“I think it would send out a really powerful message to all sports and governing bodies that we can be inclusive and we have to look at how far we have come as well.
“Five years ago we were playing our finals on Court 17 and to have Court One packed out was a really special moment for us.
“But what it did for wheelchair tennis and the growth of the sport is even bigger.
“I think if that was to happen it would break new ground and as tennis players it would be an absolute dream.”
Hewett and Reid are supporting Play Your Way To Wimbledon – a national competition with regional and county rounds, which sees winners get the chance to play at SW19.
This year’s competition includes a new junior wheelchair category, which joins an adults’ doubles pathway, visually impaired, wheelchair and learning disability tennis.
Reid added: “The great thing about it is, the message we are trying to send is that tennis is for everybody.
“When you have an event like this, which has been going for a long time, to have categories like this, which mean it’s more accessible hits the message home a little bit.”
:: Vodafone, Official Connectivity Partner of Wimbledon, is working with Alfie Hewett and Gordon Reid to inspire the next generation of tennis players through Play Your Way To Wimbledon.
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