Probably his marriage would be decided during the war. Georgios was mentioned as a possibility for Elisabeth of Romania about a decade before they actually wed, and Elisabeth didn't think much of Georgios ("God started the prince, but forgot to finish him"). So, if that marriage hasn't gone through, Alex might marry her. If it has, then Alex might marry someone else, assuming that WW1 goes as OTL, I'd say the possibility of Alex marrying a German girl is slim. If she's from one of the more British leaning families (Württemberg/Teck; Welf; Battenberg, etc.) it might be considered as thin edge of the wedge. A Russian match would have no purpose since a) any girl is likely to be related to him in someway and b) there are already enough Romanov-Greece marriages.
He might get a match with a princess from another Balkan state - Yugoslavia or Bulgaria (one of Tsar Ferdinand's daughters is available IIRC), but it really depends when he marries (before, during or after the war).