The former Scunthorpe boss is a free agent after a seven-game spell in charge of Shamrock Rovers ended on Friday night.
He had been appointed interim director of football, in charge of team affairs, until the end of the Irish season.
Shamrock won four and lost three under Laws, with notable wins including the 7-0 thrashing of Dundalk and 2-0 success at league champions Sligo - managed by fellow former Iron boss Ian Baraclough - on Friday.
Hartlepool, bottom of League One, are searching for a new boss after Neale Cooper's resignation last week.
Bookmakers Skybet and Stan James offered odds on who would replace Cooper, with Laws initially as long as 10-1 on Thursday evening.
Skybet suspended betting on Saturday morning after a steady steam of bets on Laws, while Stan James had cut their odds from 6-1 to 1-6 by Sunday afternoon.
Laws left the Iron in November 2006 after being approached to take charge of Sheffield Wednesday, ending an association of more than eight years with the club. He quit in 2004, but was reinstated following a boardroom coup which saw Steve Wharton return as chairman and oust his replacement Chris Holland.
He twice led the Iron to promotion from what is now League Two, as play-off winners in 1999 and runners-up in 2005.
After managing Wednesday he also had a short spell in charge of Burnley, taking charge with them in the Premier League but was unable to prevent the Lancashire side dropping back to the Championship.