The North Londoners are yet to make a signing during this summer, with the transfer window set to shut on August 9 as opposed to the end of August.
Bale's Real Madrid future, meanwhile, has been unclear this summer, with conflicting reports over where the Welshman will be plying his trade come the autumn.
When asked by a Spanish reporter if Bale could be a target for Tottenham, Pochettino laughed and replied: "I think it's not realistic."
However, the Argentine added: "With or without injuries, I think that's our target [to bring in players] after finishing last season.
"We want to add some quality who can help us to achieve the goals we want. We are going to see what happens in the next few days."
Spurs, who suffered an International Champions Cup penalty shootout defeat against Barcelona in California on Saturday, are currently without nine players who featured in the World Cup semi-finals.