India sets 194 for victory closed day three on 110-5, with captain Kohli unbeaten on 43.
He made 149 in India’s first-innings 274 and steadied India after they slipped to 78-5 on Friday at Edgbaston.
“No-one is invincible in world cricket. We can get him out,” said Anderson, England’s leading wicket-taker.
“If he bats like he did first innings, even batting with the tail, it was so hard to keep them on strike.”
Anderson dismissed Kohli four times in 10 innings on India’s previous tour of England in 2014.
However, Kohli adjusted his technique, playing more on the front foot, in order to negate the moving ball.
“I’ve been encouraged by the way I’ve bowled at him in this game,” said Anderson, who had Kohli dropped on 21 in the first innings.
“I found the edge a few times in the first innings. On another day I could have got him and we could be in a much different position now.
“But that’s not the case. We’ve just got to go away and know we can get him.”
England collapsed to 87-7 in their second innings on Friday before Sam Curran’s 63 helped them to 180.
Stuart Broad took two wickets in two overs as India slipped to 78-5 in pursuit of their highest successful chase in England.
Anderson said of Curran: “I remember me as a 20-year-old, and I didn’t know what was going on. I was in awe of everyone.
“But he’s been around quite a bit and he knows his game really well for a young lad.
“He’s obviously got a little bit of fight in him as well. To go out in that situation and show the guts and determination he did, was brilliant to see from such a young guy.”
Anderson, Curran and Ben Stokes claimed a wicket apiece but Kohli and Dinesh Karthik’s unbroken 32-run stand left India needing a further 84 to win on Saturday.
“A couple of early ones tomorrow and both teams will be a bit nervous,” left-arm seamer Curran told Test Match Special.
“We are trying to get everyone out. It will be a crucial first hour tomorrow.”
India pace bowler Ishant Sharma took 5-51 including three wickets in an over to undermine England’s second innings.
He said Kohli’s continued presence gives India “a lot of confidence” that they can take a 1-0 lead in the five-match series.
“Virat has scored 150 in the last innings,” said Ishant. “Cricket is such a game that you can chase down small totals easily with one big partnership.
“He is someone who always gives you positive energy and that is a big thing as captain. He always wants to do something special for team India.”>