I think Mary Stuart, Queen of Scots was the only other serious Catholic contender.However the plan seems to have been to marry Elizabeth off to a catholic instead, making her a more suitable Queen. Mary Queen Of Scots continued to be a threat after Elizabeth's concession to the throne - hence her execution at Fotheringhay. As a daughter of Henry VIII, Elizabeth had the legitimate claim ( although some catholics refused to recognise the marriage of her mother Anne Boleyn to Henry VIII)
The English Catholics wanted Mary Tudor to name Mary Stuart or Mary Queen of Scots as the next heir to the throne. Who had the leditimit claim? Elizabeth because she was next in line to the throne, then it was Mary Stuart