They will host south coast rivals Southampton, in ninth spot, on Sunday.
"I'm not sure about that," Howe told the Daily Echo when asked whether Leicester's success had inadvertently heaped more pressure on his shoulders.
"I think it's all down to your club and how you are run -- and what your owners see for the future of the club."
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Wins for Everton and West Bromwich Albion, while a draw for Southampton on Wednesday meant that Bournemouth dropped to 10th in the table after 16 games.
"I have to say the guys here have been excellent with me in terms of the expectations they place on us," said Howe. "Every club is looking to win the league. Naturally, if that is a possibility, we would look to do it.
"But I think for a lot of the clubs in the Premier League, it is about consolidating their position. Making sure we are still able to compete at this level, first and foremost, has to be our target.
"Then, beyond that, anything else that comes we will look to do it."
(Reporting by Shravanth Vijayakumar in Bengaluru; editing by Sudipto Ganguly)
