The daily Rheinische Post said Schäuble, of Merkel's conservative Christian Democrats, had signed on for another four years.
The 71-year-old veteran, one of the main architects of Germany's tough-love response to the eurozone crisis, has served in the post since 2009.
However the make-up of the cabinet, further details of which were leaked to other German media outlets, is still dependent on the outcome due of a binding vote by the nearly 475,000 members of the Social Democrats (SPD), set to become junior partners in Merkel's "grand coalition" government.
If the "yes" votes win, several reports said Frank-Walter Steinmeier, 57, of the SPD would return to the foreign ministry, where he served during Merkel's first term from 2005-2009.
Steinmeier would then give up the leadership of the SPD's parliamentary group and hand the reins to his chief whip, Thomas Oppermann.
Party leader Sigmar Gabriel, 54, is due to become Merkel's vice-chancellor and take the helm of a "super-ministry" in charge of the economy, Europe's biggest, as well as Germany's ambitious energy transformation away from nuclear power and toward renewables.
The SPD has pledged to appoint women to half its cabinet seats.
Left-wing firebrand Andrea Nahles, the SPD's general secretary, is to become labour minister, according to the reports, and party vice-chairwoman Manuela Schwesig is to take charge of family affairs.
SPD treasurer Barbara Hendricks is headed for the environment ministry.
Party sources declined to confirm the reports, saying that they would wait until the results of the SPD vote are announced before publishing the cabinet list.