The Sun says Rovers have already been turned down once by Tottenham chairman Daniel Levy.
But Rovers will not give up and Sherwood, 43, is seen as the man who can re-energise Ewood Park following the club's relegation and the departure of the unpopular former boss Steve Kean.
Rovers are willing to pay Sherwood £2million- a-year, which is double what he is on at Spurs.
Sherwood is the technical co-ordinator at Spurs and was given a new four-year deal last month. Levy values his work, which is why he is unwilling to let him go.