The 23-year-old Mendis destroyed India's top order in the Asia Cup final earlier this month with a magical spell of 6/13 in his eight mesmerising overs, but Kumble sounded confident that his strong Test line-up can cope better than the one-day team.
''He is something we need to watch out for, although we respect every bowler we face,'' Kumble said at a media briefing after the team's arrival here yesterday.
''Test cricket is different and we have the quality. Our middle-order has more than 30,000 Test runs and four of them have played more than 100 Tests,'' he added.
India's most successful Test bowler, Kumble pointed out that unlike in ODIs, the batsmen can take a good amount of time to get settled in the longer version of the game.
''In Tests you get more time to figure out the bowler. It will be challenging, but I am sure our batsmen will cope,'' he added.
Kumble further expressed his pleasure to have a full-strength bowling line-up with Zaheer Khan and Harbhajan Singh coming back in to the side, for what he expected to be a tough series.
''We have Zaheer Khan back in the team and his experience in the subcontinent conditions will be useful for us,'' said Kumble.
''There is also Ishant Sharma who has really progressed well as a seamer and we have Harbhajan Singh back as well."
''We have had a good combination and in the last one year or so we have been really consistent with our performances, that's something which we will take forward.
''Whenever we tour Sri Lanka it's always been tough. It will be a lot of hard work and we are ready for that.'' India will begin its tour campaign with a three-day practice match against Lanka Board XI on July 18.
The first Test will be played at the Sinhalese Sports Club in Colombo from July 23.