Crooks, who played for Spurs from 1980 to 1985, was impressed with the Arsenal-owned defender’s performance against Crystal Palace away from home in the Premier League on Saturday afternoon.
The England international right-back scored a goal, had a pass accuracy of 90%, created one chance, put in three crosses, and made two interceptions, seven clearances and one block.
Former Tottenham man Crooks has included Jenkinson in his BBC Premier League Team of the Week and has spoken highly of the 23-year-old.
“Carl Jenkinson appears to be having one hell of a rollercoaster ride in the claret and blue,” the 57-year-old wrote on BBC Sport. “During his short but eventful time with the Hammers he's been sent off, left out, substituted and given away a penalty against Crystal Palace. Nevertheless, this lad keeps bouncing back.
“His ability to shake off these occupational hazards and still try to get among the goals is quite astonishing.
“His finish at Sunderland last week might have been perceived as a fluke but his goal against Crystal Palace smacks of a full-back developing a taste for the art. A player with a terrific will to succeed.”
Jenkinson joined West Ham on a season-long loan deal from Premier League rivals in the summer transfer window.
The Englishman was successful in his first loan spell at the Boleyn Ground last season, but so far this campaign his performances have been mixed.
The former Charlton Athletic man has scored two goals and created five chances in seven Premier League appearances so far this campaign.
Jenkinson has a pass accuracy of 80% and a shot accuracy of 50%, and has won six headers, two dribbles and seven tackles.