I seem to recall in a book on the Goring/Danish by Ken Smith that he recommended 1.e4 e5 2.d4 exd4 3.c3 Qe7 4.cxd4 Qxe4+ 5.Be2. I can't find too many games in this line, but according to the chessbase database it's been played 5 times, white winning 3 and drawing 2. Furthermore, it was the preferred move of Rudolf Spielmann, and Alekhine himself played it on one occassion.
If white doesn't want to continue in gambit style, 4.Bd3 looks good enough for an edge, and 4.Qxd4 looks okay for white too. But either 5.Be2 or 5.Be3 would be the gambiteer's preference, and they both look quite promising for white.
[Event "Ostende-B"]
[Site "Ostende"]
[Date "1907.??.??"]
[Round "2"]
[White "Spielmann,Rudolf"]
[Black "Billecard,Moritz"]
[Result "1-0"]
[Eco "C21"]
1.e4 e5 2.d4 exd4 3.c3 Qe7 4.cxd4 Qxe4+ 5.Be2 Bb4+ 6.Nc3 Nf6 7.Nf3 0-0 8.0-0 Qe8
9.Re1 Qd8 10.Bg5 Bxc3 11.bxc3 d5 12.Qb3 c6 13.Bd3 Nbd7 14.Ne5 h6 15.Bh4 Nb6 16.Re3 Qd6
17.Rae1 g5 18.Bg3 Qd8 19.Bb1 Ne4 20.f3 Nxg3 21.hxg3 Qf6 22.Qc2 Qg7 23.f4 Nc4 24.Nxc4 dxc4
25.fxg5 hxg5 26.Re5 Bd7 27.Rxg5 1-0
[Event "Vevey exh"]
[Site "Vevey"]
[Date "1925.??.??"]
[Round "0"]
[White "Alekhine,Alexander"]
[Black "Cheron,Andre"]
[Result "1-0"]
[Eco "C21"]
1.e4 e5 2.d4 exd4 3.c3 Qe7 4.cxd4 Qxe4+ 5.Be2 Qxg2 6.Bf3 Qg6 7.Ne2 Ne7 8.Nbc3 c6
9.Nf4 Qd6 10.0-0 f5 11.Re1 Qc7 12.Qb3 Na6 13.Ncd5 Qa5 14.Re5 cxd5 15.Nxd5 Kd8 16.Bg5
1-0
Regards, and Happy New Year,
Craig