Clarets gaffer Owen Coyle has been fairly busy in the market so far, adding striker Steven Fletcher, utility man David Edgar and defender Tyrone Mears to his playing pool at Turf Moor.
He is aware he needs a strong squad ahead of their Premier League survival bid, though, and he likes the look of Rovers star Mills.
The 22-year-old caught the eye last season and has several admirers, including Birmingham, Wolves and Nottingham Forest, with Forest recently having a £2million bid for his services rejected.
Wolves boss Mick McCarthy may cool his interest in Mills having landed Marseille defender Ronald Zubar for an undisclosed fee.
But Doncaster chairman John Ryan insists the club "are not interested in selling Matt Mills", so will not budge on his valuation of £3million.