The screenshot of next month's free games was taken by NeoGAF user matrixman92 via Expert Zone, a Microsoft website. The image lists the free Xbox 360 games as Tomb Raider being offered from 1st-15th March, and then Bioshock Infinite from 16th-31st March.
The Xbox One games are stated as Rayman Legends, and February's free game, #IDARB, will also be available throughout March too.
As mentioned earlier, the screenshot of the statement notes that this April will offer up double the free games. This means the Xbox 360 and Xbox One will have a total of four games each for free download throughout April.
Nothing has been officially announced from Microsoft through its usual channels, so we would urge you to take this leak with a pinch of salt. However, Microsoft usually announce their free game lineups a few days before the end of the month, so we expect to hear if this is all true before Sunday.