As per a report in Daily Mail, Archer is set to be offered a year-round, multi-million-pound deal by the five-time IPL winning team that would require the ECB to gain permission from the IPL franchise to pick him for England's international matches.
Archer is a doubt for the Ashes starting at Edgbaston on June 16.
England fast bowler Jofra Archer has also entered the auction but is unlikely to play as he continues his recovery from elbow surgery.
Barbados-born Archer last played for England against India in a Twenty20 match in March.
England are a brilliant team despite the absence of pace bowler Jofra Archer and all-rounder Ben Stokes, said the wicketkeeper-batter.
The T20 World Cup will be held in October-November and the Ashes series will begin from December 8.
Archer's absence dealt a major blow to Royals who also had England's Ben Stokes ruled out for the season after the all-rounder broke his finger in their opening match.
The England pacer went under the knife to remove a glass fragment from a tendon on his right hand on Monday after an attempt to clean his fish tank went wrong.
Pant attained cricketing immortality by playing 'reverse scoop' while facing two of the top fast bowlers in the world - James Anderson and Jofra Archer.
Archer will also miss the early part of this year's Indian Premier League.