"We have had an amazing fortnight at the Rio Olympics and we should be looking at the differing ways that we can recognise and reward the athletes for all they have achieved, and honours are there to recognise and reward people," Ms May's spokeswoman said.
Track champion Mo Farah has admitted that he would be thrilled to receive a knighthood after his "double double" success at Rio.
"I didn't even dream of becoming Olympic champion, let alone four times," he said.
"Anything is possible but for me it is up to the public. I just have to enjoy what I do and keep winning medals for my country because I just love winning but being Sir Mo would be amazing.
"I remember Sir Alex Ferguson got it because he was at Manchester United, and Sir Steve Redgrave for what he did, and to be able to be in the same category as them would be pretty amazing."
Tennis player Andy Murray is expected to be made Sir Andy, following demands for a knighthood after he first won Wimbledon in 2015. Heptathlete Jessica Ennis-Hill could also be made Dame Jessica.The Queen yesterday led the praise for Team GB and Northern Ireland on their "outstanding performance".
"The outstanding performance of Team GB reflects the talent and hard work of the athletes and their support teams," the Monarch said. "I send my best wishes to all those who contributed to this remarkable achievement."
A party is being organised for British medal winners at Buckingham Palace this autumn; the Queen is Australia's Head of State but the party is confined to those winning athletes and staff from the UK.
A street parade is also being organised in both London and Manchester, and Royal Mail is under pressure to have gold mailboxes installed in the suburbs where gold medallists hail, as they did in 2012.
The Queen's message follows that of Prince William and Duchess of Cambridge Kate and Prince Harry, who declared the athletes had "made the entire country proud".
The level of Olympic funding in Britain has leapt since Sydney 2000 where 58.9 million pounds ($101.4 million) was spent to win 28 medals (11 gold).
About $413 million was spent for the London 2012 Games where Team GB won 65 medals including 29 gold.
In Rio, $473 million was spent and their Olympians won a record 67 medals including 27 gold.
At a cost per Briton - equating to 1.09p per year over the last four years - there is no public quibbling about the cost to the public purse.
Bill Sweeney, chief executive of the British Olympic Association, said the success was down to two decades of hard work and investment in British sport.
"It has been a brilliant Games but this is not an overnight success," he said. "Thanks to the contribution of the National Lottery players via UK Sport and their investment, this is 20 years in the making and we've now enjoyed five successive Games of medal growth. No one has come close to that and it's an unbelievable achievement."
British athletes were flown home today in a special gold-nosed British Airways 747 jumbo jet where they were all treated to three course meals and champagne and a re-run of Chariots of Fire.
Meanwhile, social media and elements of the British press have labelled Australia "cruel" towards its Olympians for complaining about the lack of medals.
