Laws, together with Preston boss Darren Ferguson, both parted company with their respective clubs earlier today.
And Howe, who is six months into a three-year contract with Cherries, has already been installed as one of the favourites to take over at Turf Moor.
Cherries chairman Eddie Mitchell, speaking to the Daily Echo earlier this evening, confirmed he had not received any approaches for Howe.
Mitchell also said any approaches would be unwelcome and added that he hoped Howe and Tindall had no desire to leave.
Howe has worked wonders in his first management post at Dean Court, saving Cherries from relegation in his first season and then getting them promoted in his second.
The 33-year-old has already rejected overtures from Peterborough and Southampton to remain loyal to Cherries.
However, Howe could be tempted by the lure of the Championship with Burnley currently ninth and just two points adrift of a play-off place.
Howe took Cherries for training this morning and was due to embark on a scouting mission to watch Brighton host Charlton tonight.
A flood of money on Howe to become the next Burnley manager saw him backed in from 6-1 to evens with leading bookmakers Victor Chandler today.