"It's a huge honour. I am humbled," the actor told the Daily Mirror in an interview published on Wednesday, three days after her triumph on 'Celebrity Big Brother'.
The 31-year-old also revealed she planned to extend her stay in Britain and was on the lookout for love.
The Daily Mirror said Shetty had been invited to a reception to mark Commonwealth Day on March 12 where she would come face-to-face with the queen.
She was also due to meet Blair and other ministers at the House of Commons, Britain's lower chamber of parliament, on February 7, the tabloid reported.
Neither the royal household nor the prime minister's office were immediately available for comment.
Shetty is hot property thanks to her appearance on the reality show, which grabbed international headlines amid fears she was being mistreated by a handful of fellow contestants.
"The row has been politicised but why wouldn't I want to meet Tony Blair?" Shetty told the Mirror.
The actor, whose Bollywood career had come off the boil, is tipped to make a fortune from her new international status.
In contrast, the three celebrities accused of tormenting her on the show, reality TV star Jade Goody, singer Jo O'Meara and model Danielle Lloyd, have spent the past few days giving tearful interviews and explaining their side of the story.
Shetty was called a 'dog' on the programme. A few of the housemates refused to learn her name, referred to her as 'the Indian' and 'Poppadom', and Lloyd said: "She should fuck off home. She can't even speak English".
Life after 'Celebrity Big Brother', however, looked bright for Shetty, with the Mirror reporting she had been approached about writing a book, appearing in films and on television.
The actor said: "I'd love to do a cookery show called: 'If Shilpa Can. Anyone Can'.
Turning to her love life, Shetty, who still lives with her parents, told the paper: "I'm single and I'm ready to mingle."
But she warned potential suitors they would face a grilling from her father before being allowed to take her out.
Shetty added: "I'm a pretty low maintenance girlfriend, all I ask for is that he buys me lots of diamonds!".