On Friday, Lemieux (34-2, 31KOs) won the vacant IBF title with a unanimous 12-round decision over Cameroonian Hassan N'Dam.
The 33-year-old Golovkin (33-0, 30Kos) has dominated the middleweight division since winning the WBA title in July 2009 when he knocked out John Anderson Carvalho in the second round.
In a chat with TVA Sports, Lemieux said that he did not fear anybody in the division including Golovkin but it all depended on the money on offer.
"I will face him, do not worry – but everything should be correct financially. I want to face all of the best opponents in my division because I know I'll beat them.
"They are strong guys, but I will dominate if I train properly. There are several good boxers at middleweight, but if I train hard there are no limits.
"Everything depends on the negotiations, but these are the guys that I want to face," Lemieux told TVA Sports.