The account is worth £3.6m in the UK according to Nielsen Media Research, with ad spend recently been hiked to target health-conscious consumers.
It is understood the review is being conducted out of the headquarters of the brand's parent company Vandemoortele in Belgium.
Alpro currently manufactures a range of soya-based products including drinks, desserts, a dairy-free alternative to single cream and yogurts.
Other brands in the Vandemoortele stable include fellow soya-based brand Provamel and the Belsoy range in the United States.
The advertiser tends to weigh its promotional activity heavily on television activity and traditional sampling at exhibitions and fitness-based locations. Alpro promotions used the straplines "Fuel your body, mind and soul" and "Soya, but not as you currently know it".
Alpro recently launched a super-light version of its soya milk product at London Fashion Week using sampling to consumers. This month it signed a partnership deal with Holmes Place, which saw the brand looking to target a more mainstream audience as well as fitness-focused people over 25.
The offer included a free Alpro chiller bag, that was handed out to members of Holmes Place as part of the promotion.
Neither The Point or Alpro were available for comment.