FRANKFURT—The European Central Bank is "seriously" considering taking its rate on overnight bank deposits into negative territory, a top member of its executive board said Wednesday, adding to mounting speculation that the central bank will act at its next policy meeting to keep the tepid euro-zone economy on track.

"[Negative rates] is something we are considering very seriously," Benoît Coeuré, ECB executive board member, told news agency Reuters in an interview, adding that it is "a very possible...