The Bears have one Top 30 place left for 2027 and are preparing a $1 million-a-year offer for Matt Burton.
Meninga's club is weighing a four- or five-year deal.
Burton wants to play five-eighth, but Canterbury will not use him there.
Bulldogs football director Phil Gould has said Burton does not want to leave and the club does not want him gone.
Canterbury's salary-cap and roster balance could still prompt a 2027 move.
Meninga said Burton would be valuable to the Bears as a five-eighth.
Latrell Mitchell and Sam Walker could also be 2028 targets, although reports differ on whether Mitchell might move.
Walker's well-documented contract issues at the Roosters add to his potential as a target.
"I think Latrell is pretty happy with what he's doing at the moment, but we're always there to listen if there's an opportunity."
Meninga made the comment while discussing Mitchell.