Babar, who injured his finger during the West Indies series before aggravating the problem after being struck during Pakistan's warm-up match at Beckenham, missed the first test which England won by an innings and 103 runs.
"Babar batted in the nets, faced fast bowlers, spinners and throwdowns," Gul told reporters. "We're hopeful he will be available for the game and today he was looking good; he batted well in the nets. He had a full batting session."
His return would provide a timely boost for Pakistan after a batting collapse in the first test at Headingley, where England bowled the tourists out twice in fewer than 86 overs.
Babar was Pakistan's leading run-scorer in the preceding series against West Indies, scoring 193 and registering two half-centuries.
England lead the three-test series 1-0, with the second test set to begin on Thursday.