The 26-year-old, who is out of contract this summer, has been offered a new deal by Ipswich but is also wanted by Sunderland and Crystal Palace.
"Tommy has not ruled out signing a new deal with Ipswich, that is still a very strong option," Miller's father Tommy senior told BBC Sport.
At the weekend Miller married his long-time girlfriend and will make his final decision after returning from his honeymoon on June 21.
"The Ipswich chairman David Sheepshanks called him before the wedding to wish him all the best," added the midfielder's father.
"While he is away he is going to think what is best to do.
"There have been lots of reports linking him with Celtic, but I've heard absolutely nothing on that front."
Miller joined Town from Hartlepool in an £800k move in the summer of 2001.