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The sixth seed is leading the odds with some bookmakers, despite only reaching the second week for the first time after a 6-4 6-1 win against Greece's Maria Sakkari.
No British woman has won the singles title since Virginia Wade in 1977.
"I'm pretty sure favourites come and go and change daily. I'm just happy to be here," said the 26-year-old.
"I don't spend too much time thinking about that kind of talk or listening to it."
Eighteen-time Grand Slam winner Chris Evert and Britain's former Wimbledon semi-finalist Tim Henman have been among those to say they think Konta can come close to matching Wade's achievement.
Konta goes onto play French 21st seed Caroline Garcia, who beat the world number seven in three sets at Indian Wells earlier this year.
Second seed Simona Halep or former world number one Victoria Azarenka, who beat Konta's fellow Briton Heather Watson, wait beyond Garcia in a tough section of the draw.
But Konta, who had only won once at Wimbledon before this year's run, says there is still room for further improvement in her game.
"I'm playing some good tennis but I don't think I'm playing unbelievable tennis," the Australian-born player said.
"I'm just playing with the mindset of getting better like I have done in every match of my career.
"I believe in myself that I can keep improving and getting better."
She added: "It is a massive compliment to have former players of that calibre thinking that highly of me."
British number two Watson, who was a set up before losing to Azarenka, believes there is no reason why Konta cannot win in SW19.
"I think she can win a Slam," Watson said. "She is playing brilliant, so aggressive, so solid and always plays well on the grass."
Mary Pierce, former French Open champion on BBC Radio 5 live:
Johanna Konta walks around the court very confidently and having the crowd behind you like she has is a big extra factor.
It's very nice to see her play this way and she is definitely a contender for the title.
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Watson, 25, said she was "very upset" after failing to reach the second week of a Grand Slam for the first time.
She pushed two-time major champion Azarenka, who is playing her first Slam since giving birth in December, all the way before losing her serve at 4-4 in the final set as the Belarusian saw out victory.
It was a chastening defeat reminiscent of Watson's thrilling three-set loss against top seed Serena Williams on Centre Court in 2015.
"I have been feeling great about my game and I feel I have fallen at the same hurdle again. It hurt a lot today," said the Guernsey player.
"I really wanted to make that push for the second week. I gave myself a chance today and I didn't take it."
However, Watson did get the better of Azarenka when they met again later on Friday in the mixed doubles.
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Watson and her Finnish playing partner Henri Kontinen, the reigning champions, won 6-3 6-4 against Azarenka and Serbia's Nenad Zimonjic.
"I definitely didn't want to lose to her twice in one day so I was pleased to get through that," said Watson.
Watson has dropped to a ranking of 102 after a difficult start to the year, but an impressive grass-court season - which included a run to the Eastbourne semi-finals - will see her rise back into the top 100.
"Getting back into the top 100 was one of my goals by the end of grass-court season. I'm very happy with that," she added.
"I feel like I'm underachieving at the moment."
British number one Johanna Konta says she is ignoring being labelled as the favourite to win the Wimbledon title.