India resume their second innings still 451 runs behind England's first innings total and spin is expected to play a major part in the final two days of the third Test.
However, leg-spinner Mishra believes that India's batsman are more than capable of dealing with the spin threat of Swann.
"Yes the wicket is offering turn now but we have players who play spinners well," said Mishra.
"The batting has depth and I don't see any problem in handling Swann."
Mishra took 3 for 150 off 43 overs in England's first innings total of 710 for 7 declared.
England can replace India as the world's number one side in Test cricket with victory at Edgbaston this weekend.