Four Corners reported that Mr Pike, who represents the Queensland seat of Bowman, arrived at Mrs Rinehart's $34 million Sunshine Coast beach house in January to find One Nation leader Pauline Hanson, her then chief-of-staff James Ashby and federal MP Barnaby Joyce staying there.
Coalition sources told the program that during the lunch, Mrs Rinehart asked Mr Pike whether he was thinking of joining One Nation or would ever consider it. The LNP member saw it as an active attempt by the billionaire to recruit him to the party.
Mr Pike declined to be interviewed by Four Corners but issued a statement.
"I have enormous respect for Mrs Rinehart and all she has achieved," he said. "But I am, and always will be, a Liberal. I believe in the Liberal Party, in our leadership, in our values that shaped modern Australia, and in our ability to do it all again. Australia's future is too important for political opportunism."
Mrs Rinehart did not respond to Four Corners' questions about whether she tried to recruit Mr Pike or other Coalition MPs to One Nation.
The report comes amid questions about the extent of Mrs Rinehart's support for One Nation. In April, she gifted the party a plane worth more than $1.5 million, while two of her executives, former NT chief minister Adam Giles and professor Ian Plimer, each gave the party $500,000. Mr Giles also donated a Ford Ranger ute.
Senator Hanson has acknowledged consulting Mrs Rinehart on policy. "My policy on pensioners being able to work unlimited hours and without losing their pension or their health care card came from Mrs Rinehart," she told ABC Radio in Perth.
The report noted Mrs Rinehart, Australia's richest person with an estimated fortune of about $39 billion, has praised Senator Hanson and hosted fundraisers for the party. Professor Plimer's largest previously disclosed political donation was $50,000 to the National Party.