However, the royal couple are yet to visit the Scottish town, despite an official invite being sent.
Civic and commercial leaders have been left disappointed by the apparent snub, reports the Daily Record.
Harry is the third Earl of Dumbarton after the peerage lay dormant for almost 300 years.
However, 435 days after he was given the title, he and his wife are yet to take up the offer of the Lord Lieutenant of Dunbartonshire, Michael Gregory OBE, to visit the region.
A source told the Scottish paper: “It’s understood that Harry and Meghan have been invited by the Lord Lieutenant but they have yet to accept it.
“A visit from them would no doubt give the area a boost. It’s something people had been looking forward to.”
Of whether there were plans for the new royal parents to visit, Gregory said: “At the moment all I can say is they are not.”
However, he added that it does “not preclude a visit in the future”.
Harry, 34, and Meghan’s two-month-old son Archie would be entitled to inherit the Scottish earldom, although the couple have said they would not be accepting titles for him.
It had been thought the Duke and Duchess, 37, paying a visit to the area would give a boost to local businesses and tourism.
Their absence from Dumbarton contrasts with their official visit to Sussex last October.
Of their future Scottish plans, a palace source said: “Harry and Meghan hope to visit the area within the next year.”
Before Harry was given the ancient title, it had not been in use since 1749.