"It is possible in football if you believe," Pochettino told a news conference on Thursday.
"Harry is a player with a character and personality who believes in all. He's a person that never settles the limits, he is open to improve and yes, why not?"
Second-placed Tottenham, who are on a six-game winning run, host Bournemouth in the Premier League on Saturday knowing that victory would allow them to cut the gap on Chelsea to four points before the leaders face Manchester United on Sunday.
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Pochettino wants his team to focus on the task at hand when they meet Eddie Howe's 15th-placed side, who are slipping closer to the relegation battle after picking up only two points in their last three games.
"It is important for us to get the three points more than to put pressure on Chelsea," the 45-year-old Argentine said. "Our target on Saturday, our challenge, is to win the three points and then we will see what happens."
Midfielder Victor Wanyama is back in contention for Spurs after recovering from a back injury, while goalkeeper Michel Vorm and defender Cameron Carter-Vickers, who are both carrying knee injuries, have been ruled out.
(Reporting by Hardik Vyas in Bengaluru; editing by Mark Heinrich)
