Kuwaiti Information Minister Muhammad Abu al-Hasan on Monday said his ministry had approved a request by the Rotana Art Production company to sell the tapes in the emirate, the daily al-Rai al-Am reported.
Rotana is owned by a number of Saudi investors headed by tycoon Prince al-Walid bin Talal.
All Iraqi cultural production was banned by Kuwait, following the emirate's invasion and occupation in 1990 by troops of former president Saddam Hussein who was ousted in April by a US-led invasion force.
Al-Sahir is very popular in Kuwait as in other Arab countries, but was criticised for his perceived support of Saddam Hussein in spite of the fact he had never sung in praise of the former Iraqi leader.
Abu al-Hasan, however, said no one has yet approached the ministry for approval to invite al-Sahir to perform in the emirate.
Kuwaitis breathed a sigh of relief at the overthrow of Saddam and many are eager to see ties normalised with the new Iraq, but some, including a number of MPs, urge caution in dealing with Baghdad.