But Levy is adamant that the duo will not be allowed to leave White Hart Lane at the end of the season.
The goals took the 24-year-old's tally for the season to 18 in just 19 games - he has since played twice more in January - and to the top of the Premier League Golden Boot race.
"Until today, now, no-one is close to arriving in this transfer window", Pochettino said.
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Gandhi is scheduled to launch the first leg of his party's poll campaign in Karnataka on February 10. It will not be a contest between me and (Prime Minister) Narendra Modi.
Spurs chairman Levy this week stated he is "100 per cent confident" the north London side will retain their prized assets, both this month and during the off-season transfer window. Manchester City and Manchester United are scrapping over Arsenal's Alexis Sanchez while Liverpool have already bought Virgil van Dijk and sold Philippe Coutinho.
"You know better than me that if you want to sign players to help you, there must be an opportunity and it's hard to find this opportunity", Pochettino said. The manager believes that opportunities to make shrewd January signings are limited.
Their attention will now be on their Premier League game at home to Everton on Saturday as they look to keep pressure on the teams above them. They sit three points adrift of fourth-placed Liverpool in the table.
Midfielder Harry Winks is a doubt against Everton because of an ankle injury, Rose is set to miss out because of a knee problem while centre-back Toby Alderweireld is working his way towards a comeback from a hamstring tear sustained in early November.