De Allende started the Springboks final against England on Saturday and was one of the standout performers for South Africa during the competition.
The abrasive centre is set to join Panasonic Wild Knights before re-joining the Stormers later during the 2020 Super Rugby season.
According to the report, he will then link up with Munster ahead of the 2020/21 season after signing a two-year deal with Johann van Graan's men.
De Allende will follow in the footsteps of Jean de Villiers, who also signed for Munster (in 2009) after tasting success with the Springboks at the 2007 Rugby World Cup.
The centre would still be eligible for the Springboks as there is no restrictions on overseas based players in South Africa.
De Allende has won 45 test caps for the Springboks since making his debut in 2014.