The Mariners boss had a long association with the Rose, enjoying a testimonial and winning the Scottish Cup twice in 2007 and 2010 with the West Lothian side.
The Rose are looking for a new manager after Mark Bradley was sacked following their 6-2 defeat to Musselburgh at the weekend.
The Mariners, who could go top of the Premier Division with victory against Newtongrange Star on Tuesday, said there had been no official approach from the Rose, but suggested for them to look elsewhere for Bradley’s successor.
The club’s football secretary Tony Smith said: “There’s been no approach at all and I don’t think it would be worthwhile for them to do so.
“I had a long conversation with him and he is very happy with things here.”
Herd has been in charge at Camelon for three years and guided them to South of Scotland Shield success in their first year since moving to the revamped East of Scotland league last season.