The Blues were pitted against the Red Devils in Wednesday night’s draw after they thrashed Grimsby Town 7-1 in front of their home fans at Stamford Bridge to book their place in the next round.
Manchester United progressed through on penalties after a 1-1 draw with Rochdale at Old Trafford on Wednesday night.
The Red Devils will now travel to Stamford Bridge to take on the Blues in the fourth round at the end of October.
And Chelsea FC boss Lampard has warned his side that they will face a tough test in front of their home fans if they want to progress past the Red Devils.
Speaking at his post-match news conference on Wednesday night, Lampard said: “Two big teams. I am pleased we are at home.
“A lot can happen in football in a short time and this next round of the draw is not coming tomorrow.
“Man United have good players and they beat us 4-0 at the start of the season, albeit it was not like a 4-0, so it is going to be a tough game.”
Chelsea FC will return to Premier League action this weekend when they host Brighton and Hove Albion in front of their home fans on Saturday afternoon.
The Blues are aiming to win their first Premier League game at Stamford Bridge under Lampard this season after having struggled for consistent form in the top flight so far.
MORE: Man United latest news
MORE: Arsenal latest news
MORE: Chelsea latest news
MORE: Liverpool latest news