Stags were hoping for a glamour tie with one of the Premier League big guns, but will instead face Chris Wilder's Boro side, who sit ninth in the table, as they bid for a third giantkilling in a row after knocking out League One clubs Sunderland and Doncaster Rovers.
“It's nice to be at home, first of all, with a good top-half Championship side as our opponents,” said Stags boss Clough.
“Without wishing to sound being disrespectful, it's not a Chelsea or a Manchester United, but it is at home and we have a chance of getting through.
“We'll obviously be watching Middlesbrough closely in the next few weeks. They'll bring a very good following and it'll make for a great atmosphere.
“I think it'll be a good crowd overall and a good atmosphere, and a real test for us.
“Their priority will be to get promoted, but I have never known an easy game against one of Chris' teams.”
The third round will take place over the weekend of Friday, 7th January to Monday, 10th January, with winning clubs picking up £82,000 from the competition prize fund.
Stags earned another £34,000 from Saturday's superb 3-2 at Doncaster Rovers, backed by over 3,300 away fans.
Stags last faced Boro in the FA Cup at home back in January 2008 in a fourth round tie which saw the visitors win 2-0.
But it was quickly back to League Two focus this week as Stags were scheduled to take on Carlisle United at home last night with Salford City the visitors this Saturday.
Big-spending Salford have had two wins and two draws in last four League Two outings and play away at Barrow tomorrow night (Wednesday), but boss Gary Bowyer knows their current mid-table place is not good enough for their budget.