Ms Dorries said she was standing down as the MP for Mid Bedfordshire in June but later said she would not formally resign until she got more information about why she was denied a peerage.
Under his proposals, first reported by the Financial Times, Sir Chris said a motion could be tabled in Parliament requiring an MP to attend the Commons on a certain date.
Sir Chris, who chairs the Commons standards committee, said the move had basis in a parliamentary rule from 1801 stating that "no member do presume to go out of town without leave of this House".
Sir Chris said he had discussed his proposals with both the Conservative and Labour whips, who help organise each party's contribution to parliamentary business, as well as the Clerk of the House, who advises on procedure.
Asked if he would table a motion to oust Ms Dorries when Parliament returns in the autumn, Sir Chris said: "Maybe she'll turn up on the first day back in September and take part in debates and so on.
A close ally of Boris Johnson, she has accused Mr Sunak's political team of removing her name from the former prime minister's resignation honours list.