The Mirror reports that Allardyce has made a cut-price offer for Joselu, who is also wanted by Arsenal boss Arsene Wenger.
The Spain Under-21 international scored 26 goals for Real Madrid’s B team last season.
West Ham have offered Real Madrid a buy back price of £1.5million for next summer and £2million for 2013. The bid was rejected by Real Madrid.
Real Madrid are looking for around £7million this summer and Allardyce remains keen on the youngster.
