Radek Cerny has been understudy to Paul Robinson since joining the club in January 2005. Marton Fulop has also returned from a loan spell at Coventry City.
Nevertheless, the club want Alnwick, capped at England Under 17, 18 and 19 level as back-up for Robbo next season, according to the report, but new Black Cats chairman Niall Quinn is refusing to sell.
Spurs currently have four goalkeepers on their professional books. Former England Under-20 goalkeeper Robert Burch was on loan at Bristol City at the start of last season but couldn't break into the League One outfit's first team after one and a half seasons of injuries which restricted him to just seven reserve team appearances. On his return he made a further 13 reserve appearances before breaking his leg in the Play-Off final against Manchester United. However he signed a contract extension at the club this summer.
Burch who turned professional in July 2002 had spells on loan at Stevenage Borough twice and Woking before he became Kasey Keller's understudy for half the 2003-04 season after impressing in a summer tour of South Africa.