The midfielder, who has represented Scotland 11 times, as per Transfermarkt, has been released by Rangers and so is available as a free agent.
Kilmarnock, Bolton Wanderers and Fleetwood Town are also said to be interested in signing the 32-year-old.
Dorrans only managed three appearances across all competitions for Rangers last season, with the longest of those being 56 minutes, as he missed a total of 348 days with knee injuries, as per Transfermarkt.
His last season in English football was for Norwich City in the Championship during the 2016/17 season, in which he played 24 games across all competitions, scoring six goals and getting one assist.
Dorrans may have shown that he can be an effective player throughout his career, but it seems as though whoever acquires his services may not be able to get much game time out of him, judging by his last two seasons.
If Portsmouth do get him then they should only use him sporadically in an attempt to keep him fit across the campaign.
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