The Ibrox club have been linked with another bid to land the Jambos midfielder, having had offers rejected earlier this summer.
Rangers boss Pedro Caixinha watched Walker in friendly action against Newcastle on Friday night.
"A lot of people continue to say a lot of things, and that's it really, there isn't a situation," Cathro said.
"Jamie is happy, he is focused, he is training well, playing well. Like everyone really."
Walker, 24, has turned down the chance to sign a new Hearts contract, with his current deal expiring next summer.
And while Cathro refused to comment on reports suggesting the club have improved their offer to the player, the head coach is relaxed about the winger's situation.
"I talk to Jamie almost every day, even on days off, because he is a player I'm fond of," Cathro said ahead of his side's trip to face Elgin City in the League Cup on Tuesday.
"He is a big talent, he is someone who at a point will move on to a bigger league, a bigger club and have opportunities to work towards the top levels of the game. Of that there is no doubt.
"And I'm very happy to be playing a part in how he progresses towards that.
"But, for now, people are just wasting their time."
Walker made his Hearts debut in the 2011-12 campaign and has scored a total of 41 goals in 135 games for the Jambos.

The government introduced fees in 2013 to reduce the number of malicious and weak cases, but that led to a 79% reduction over three years.
Trade union Unison argued that the fees prevented workers getting access to justice.
The Supreme Court also found fees were indirectly discriminatory to women.
It ruled tht the government was acting unlawfully and unconstitutionally when it introduced the fees.
Unison general secretary Dave Prentis said: "This is absolutely a tremendous victory, it's probably the biggest victory of employment rights in this country."
Fees ranged between £390 and £1,200 to get a case heard at a hearing. Discrimination cases cost more for claimants because of the complexity and time hearings took.
The Supreme Court found this was indirectly discriminatory because a higher proportion of women would bring discrimination cases.
Hearts head coach Ian Cathro has played down reports of Rangers renewing their interest in Jamie Walker.
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Fees for those bringing employment tribunal claims have been ruled unlawful, and the government will now have to repay up to £32m to claimants.