Eriksen has reportedly attracted the attention of Ernesto Valverde's side due to the imminent departure of Iniesta, who confirmed on Friday he will be leaving Camp Nou at the end of the season.
The loss of the World Cup winner will leave a huge void to fill in Barcelona's midfield and Poulsen has backed Eriksen to excel if he moves to Barcelona.
Speaking to Omnisport, Poulsen said: "Of course there will be more competition at Barcelona than at Tottenham. He has got a very good standing at Tottenham right now and he has to ascertain if it is the right moment.
"Of course there will be a vacancy if Andres Iniesta leaves the club and Christian Eriksen has definitely the quality to compete on the highest level. Therefore I understand why Barcelona is interested in him."
Eriksen has been a key player for Tottenham this season, scoring 10 goals in 33 Premier League appearances, and was also the hero for Denmark in the World Cup qualifying play-offs, hitting a hat-trick against the Republic of Ireland to book a place at Russia 2018.
"Christian Eriksen is the most effective player I ever played with. All of his actions are effective – his forward passes, his finish or his corner kicks and free-kicks," Poulsen added.
"Everything is always on point and effective. I think against Ireland he only shot on goal three or four times and scored three goals. That's what makes him a class player.
"I talk about players who are very effective and who implement every situation very accurate. Christian Eriksen is one of those players. And he has got an extraordinary free-kick. He often showed it and he still shows it at Tottenham."