Barton is on the books of Premier League-bound Burnley at the moment, but he will become a free agent at the end of June.
According to BBC Sport, Rangers have made a move to sign the former Newcastle United star on a free in the summer transfer window.
The Gers, who will play in the Scottish Premiership next season after winning the Scottish Championship title this campaign, showed Barton around the Auchenhowie training ground on Saturday, according to the report.
Dyche believes that Barton will not come cheap, and has suggested that he is impressed with Rangers’ intention to sign the 33-year-old.
The Burnley boss has also revealed that he would like the Englishman to remain part of his team in the Premier League next season.
"Fair play to Rangers, it shows the clout they have, because if they're talking to him, he's not cheap,” Dyche told Sky Sports. “It shows their intentions if they see it as viable, they must be backed well.
"We've been open with our conversations with him, and his advisor, but he's still got his chance to look around and that's what players do nowadays. They're open-minded to what's out there.
"We'll give him as long as he needs. He took time to come to us last year, there were a couple of different things and he wanted to make sure it was the right place and environment.”
Barton scored three goals and created 29 chances in 38 Championship appearances for Burnley this season.
The former Queens Park Rangers midfielder had a pass accuracy of 75% and a shot accuracy of 31%, and won 67 headers, 15 dribbles and 82 tackles.