"They have to weigh their responsibilities against their consciences and then make a decision about what they want to do," Kasich said, according to The Washington Post
And Kasich spokesman Chris Schrimpf told CNN that the Ohio governor had directed the delegates he won during the primary process to remain bound to him, "unless their conscience tells them otherwise."
However, Kasich also said he is not looking to be a "disruptive force" at the convention: "Donald Trump won. It's his party and his convention," he told the Post.
Kasich senior adviser John Weaver told CNN that the comments simply make clear that Kasich believes delegates should abide by the same rules the Ohio governor himself is operating under.
At the start of the primary fight, Kasich signed a pledge vowing to support the eventual Republican nominee, but after dropping his own bid for the presidency, Kasich has declined to endorse Trump.
Schrimpf and Weaver say Kasich has not ruled out backing Trump but that the presumptive Republican nominee does not align with Kasich on a host of policy issues, as well as his use of divisive language.
Schrimpf told CNN there is still no decision on whether Kasich will participate in the convention -- which is being held in his home state in Cleveland -- but that he is not seeking a speaking slot.
The uncertainty over Kasich's presence at his own party's convention in his home state is extremely unusual and illustrates the awkward position he finds himself in.
Kasich's campaign has recently started using their email list to highlight the governor's continued high levels of favorability among the general election electorate and his efforts to help fellow Republicans.
Weaver told CNN that Kasich is "committed to a pretty exhaustive schedule" of campaigning for down-ballot Republican candidates after the convention, and he points to "what could be a troubling headwind for the party" in Trump's nomination.
Weaver acknowledged Trump has resonated with the Republican electorate, but said Kasich's popularity illustrates that a different message can also win over voters.
"The point we're trying to make is if you want to run in troubled times, here's a path that you can run on. You can run on a pro-growth, positive, inclusive agenda," Weaver says. "That message is very popular."