One media outlet suggested on Sunday that the French giants could be set to make their move for the Saints duo.
But Boyd gave those suggestions short shrift during his post-match media session following the 29-26 defeat to Exeter Chiefs at Franklin's Gardens on Sunday.
"Dan Biggar to Toulouse? Haven't they got a decent 10 (Romain Ntamack) there already?" Boyd said.
"I'm not even going to speculate on gutter journalism."
Lawes and Biggar both delivered huge showings for Saints against Exeter, with the black, green and gold having to play for 67 minutes a man down after David Ribbans was sent off.
Saints eventually took their Lions duo off, but Boyd does not believe there were any major injury issues surrounding those substitutions.
"He (Lawes) has had to overplay - we've had to play him past 60 minutes on two occasions and he's a hell of an athlete," Boyd said.
"He was in a pack that was down to seven men for the vast majority of the game.
"Lewis Ludlam, Courtney and Woody (Tom Wood) all put in tremendous shifts and all three should have been substituted really but we weren't able to help them as much as I would have liked.
"There was nothing apart from precaution in the Courtney change."
Saints confirmed after the game that Biggar was withdrawn with a mild pectoral injury but it is not thought to be anything serious.