Miller left Cardiff City for Vancouver in the summer and is reportedly keen on a short-term switch in the New Year to maintain his fitness during Major League Soccer's off-season.
St Mirren boss Danny Lennon says he has already had initial contact with the 32-year-old, who has also been linked with a move to former club Hibernian.
However, Rennie claims he has not been involved in any discussions and has questioned the benefits of letting Miller go out on loan for a couple of months.
"No one has discussed it with me," said Rennie.
"I don't see an advantage in loaning out players prior to the season. If we were presented with a case we'd consider the merits."