The Rangers and St Johnstone bosses are joined on the four-man shortlist by Scotland head coach Steve Clarke and Livingston manager David Martindale. The winner will be announced before the end of the season.
Gerrard has overseen a remarkably consistent season in which his Rangers side have lost only three of the 54 matches they have played so far.
The Ibrox club clinched the Premiership title on the first weekend in March with six games to spare, becoming Scottish champions for the first time in a decade. They are now 23 points clear of Celtic at the top of the table and just two games away from completing an undefeated league campaign.
Gerrard also guided Rangers to another impressive Europa League run in which they were unbeaten in 12 matches before losing to Slavia Prague in the last 16. The only other defeats suffered by Gerrard this season have come in the quarter-finals of the League Cup and Scottish Cup against St Mirren and St Johnstone respectively.
Rangers have not claimed the Manager of the Year award since Walter Smith lifted the honour in 2010.
Davidson, in his first season as a manager, remains on course to complete a domestic cup double with St Johnstone after leading the Perth club to their maiden League Cup triumph at Hampden in February.
They return to the national stadium this weekend to face St Mirren in the last four of the Scottish Cup and are also on course for a fifth place finish in the Premiership with the prospect of qualifying for European football next season.
Clarke, twice winner of the Manager of the Year award when in charge of Kilmarnock, has steered Scotland to a first major tournament finals since the 1998 World Cup, a place in this summer’s delayed Euro 2020 competition secured with the dramatic penalty shoot-out play-off win against Serbia in Belgrade last November.
Martindale replaced Gary Holt at Livingston in November and led the West Lothian club to the League Cup Final, where they lost 1-0 to St Johnstone, and a top-six Premiership place.