The two sides will meet at the Seddon Stadium on Tuesday 31st January with a 7.45 pm kick-off.
The game gives Town an early opportunity to avenge their 1-0 defeat at Harrison Park at the beginning of the year.
The two sides have also already met at Hollinwood Road this season with Grove fighting back from 2-0 down to claim a share of the points back in August.
In the Staffs Cup, Leek beat Stafford Rangers 2-0 back in October in the First Round whilst Kidsgrove as holders had a bye.
The victors will be at home to Hednesford Town or Stoke City in the semi-finals, whilst Rocester will face Rushall Olympic or Port Vale.