Brazil was placed in charge until the end of the season after Philippe Montanier’s sacking in January but Forest have lost five of the last seven games, leaving relegation as an alarming possibility.
Warburton has experience of the Championship from his time at Brentford, where he also worked with McParland.
The 54-year-old guided the Bees to promotion from League One and mounted a promotion push the following season. The club announced in February 2015 that they would be replacing Warburton as manager at the end of the campaign, which ended with a 5-1 aggregate loss to Middlesbrough in the play-off semi-finals.
Warburton linked up with Rangers that summer and got the club promoted back into the Scottish Premiership as Championship title winners. He also won the Scottish Challenge Cup during his spell at Ibrox.