Preston sacked Darren Ferguson last week with the Lilywhites rooted to the foot of the Championship table, and have turned to the former Hull boss Brown to keep them in the division.
Brown, 51, inherits a side that are seven points adrift at the bottom of the table.
Burnley sacked Brian Laws on the same day Preston called time on Ferguson's reign.
They have a shortlist of six candidates to be the next Clarets boss, and on Thursday night asked to speak to Lambert. They had earlier indicated they were expecting to wait until the end of next week before being able to make an appointment.
"We will be interviewing the people we want to see and hopefully moving things forward to get the next manager," said their chairman Barry Kilby.
"There is a two-week window either side of the FA Cup tie and I don`t want to belittle that because it is important we get through and keep our season alive in that sphere.
"But with two weeks and no league game with points at stake, it gives us time to get up and down the country, see the candidates we want to and get the best person for Burnley Football Club."
Crystal Palace have extended the loan of the Hull City defender Anthony Gardner until the end of the season.
The Watford forward Liam Henderson has joined the League Two side Aldershot Town on a month's loan. The Hornets left-back Mat Sadler has also extended his temporary stay at Shrewsbury Town.
Sheffield United's Richard Creswell will miss up to six weeks with the shoulder injury he suffered in Monday's 2-2 draw with Doncaster Rovers.
Swansea City have confirmed left-back Neil Taylor will be out for a month with the sprained ankle he suffered in the New Year's Day win over Reading.
The Swans midfielder Andrea Orlandi also suffered an injury in the same match, with a thigh strain keeping him sidelined for two weeks.
The Reading forward David Mooney has extended his loan at the League One side Colchester United until the end of the season.