We've only won the monthly award three times in our history with Ross Gload, Gordon, and Alexei each winning once.
Anyways there's a good chance from Abreu to win in this month, but the competition and marketability of Tanaka might be too tough. It's a two person race definitely.
For reference Semien is second in WAR among the position players and Daniel Webb is second among the pitchers.
Abreu is .259/.340/.600/.940. 21 RBIs, 7 hrs, 7 doubles, and 16 runs.
Tanaka is 3-0, 2.15 ERA, .82 WHIP, 29.1 IP and 35 Ks.
Looking at that, Abreu will probably need a bad start from Tanaka to win in April. Or just keep hitting 450 monster shots every game.
Alexei has an outside chance at player of the month if he ends on a hot streak. It'll be tough to be out Trout and Pujols though.