Cranston earned a Tony Award in the best performance by a leading actor in a play category, while the production also won the best play award.
'All the Way' dramatises late US president Lyndon B Johnson's work to pass the historic Civil Rights Act of 1964, reported Deadline.
Spielberg is now in the process of optioning writer Robert Schenkkan's play for a television miniseries.
The producer apparently wants Cranston to reprise his role as President Johnson, although it is not yet clear where the television adaptation of 'All the Way' would air.
Cranston won four Primetime Emmy Awards for his portrayal of drug kingpin Walter White in 'Breaking Bad'.