Bilic was at Craven Cottage on Saturday to see the Premier League clash with Arsenal, before appearing as a studio guest with Sky Sports on Sunday.
And Bilic insists he remains committed to his role with Croatia, having already rejected the chance to boost his wages by taking a post in the Premier League.
He said: "If I was after the money, I would have accepted the first offers that came my way from Mohamed Al Fayed (Fulham chairman) and others.
"If I have to explain my position every time I cross the border, no problem. I've been to London privately a few times before."
Bilic is still to reveal his plans for after the Euro 2008 finals in Austria and Switzerland this summer, but has denied reports that he has already turned down a new deal from the Croatian Football Association (HNS).
He added: "British media praised my position as patriotic after I told them money isn't everything and that I took up the Croatia job for a different reason.
"I do believe I am underpaid but that's not an issue at the moment and I knew exactly how much I would be paid when I took the job. It's also not true that I have turned down an improved offer from the Croatian FA.
"I've had a terrific relationship with the HNS all this time and I won't let anything spoil it. This speculation doesn't bother me at all but it could affect the team spirit."