The Shrimps were drawn away to face Spurs in Monday evening's third round draw, that a huge reward for beating Buxton 1-0 in the second round on Saturday.
Stephen Robinson will pit his wits with Antonio Conte at the Tottenham Hotspur Stadium over the weekend of January 7-10, with details to be announced in due course.
The clash will land Morecambe a big financial boost, with them getting a share of the gate receipts and broadcasting fees.
Although it is unlikely to be shown live on television, clubs get a fee for a highlights package.
Cole Stockton's first-half goal - his 16th of the season - gave Morecambe victory at Buxton in a game shown live on the BBC.
It was a potential banana skin against non-league opposition on a 4G pitch but they negotiated it.