Dollar General could launch a tender offer for Family Dollar as soon as Wednesday, these people said, asking not to be named because the matter is not public. Family Dollar, which already has a deal to sell to Dollar Tree Inc (DLTR.O) for $8.5 billion, has rejected Dollar General’s unsolicited approaches citing antitrust risks. Representatives for Dollar General and Family Dollar both declined to comment. Dollar General’s expected hostile move could lead to a protracted takeover battle involving the nation’s three largest U.S.