Barca president Josep Maria Bartomeu confirmed last week that they and Verratti were keen on a transfer, although PSG have been unwilling to hold talks.
Verratti's agent suggested that his client was trapped at Parc des Princes, prompting the midfielder to issue an apology and reaffirm his commitment to the capital outfit.
Alves, who completed a free transfer to the club on Wednesday, wants the Italy international to stay at Parc des Princes to help them realise their ambition of adding the Champions League to domestic silverware.
A word from Marco Verratti pic.twitter.com/f9cfSCpW1t— PSG English (@PSG_English) July 7, 2017
When asked about Verratti, he told a news conference: "I came here to play with him so, if he leaves, what would I do?
"This is my message to him: I hope he helps us achieve our dream. The more good players we have, the more chances we'll have to achieve it."
The 34-year-old says he was encouraged to move to the French capital both by the beauty of the city and the ambition shown by the club.
"It's not just this magnificent city that has drawn me here; this great club's ambitions are also very attractive," he told PSG's official website.
"I really like the manner in which Paris Saint-Germain have marked footballing history and continue to want the same thing, signing big players and showing a lot of desire out on the pitch. It's the sporting side of things that really made up my mind to come here.
"I have experienced a lot of different things in my life, and I think that the sum of all these experiences will help me bring something to Paris Saint-Germain. There is a lot of talent in this team, be it the youngsters who want to keep growing or more senior figures.
"There is a good balance that, I'm sure, will take us a long way and allow us to achieve our objectives."