Rovers are managerless following Paul Lambert's decision to exercise a release clause in his Ewood Park contract at the end of the campaign.
Hibernian's Alan Stubbs, Rotherham's Neil Warnock, Rochdale's Keith Hill, Hartlepool's Craig Hignett and the former Leeds United boss Neil Redfearn are also listed as candidates by the tabloid.
However, the Sun claims Riga also features highly on the Lancashire side's shortlist.
Riga managed the Addicks over two spells, saving them from relegation during a two-month spell at The Valley in 2014.
An ill-fated spell at Blackburn's Lancashire rivals Blackpool followed, before the Belgian returned to his homeland to take charge of Standard Liege.
Riga was reappointed by Charlton in January, though he was unable to repeat his trick of two years ago.