Hertha Berlin have confirmed the signing of Marseille defender Karim Rekik.
Benaglio, 33, joins the French champions as they look to replace backup keeper Morgan De Sanctis.
Verratti, 24, who has been joined on holiday in Ibiza by agent Donato Di Campli, said he "cannot talk about my future right now."
PSG have dropped their interest in Pierre-Emerick Aubameyang for AC Milan's Gianluigi Donnarumma and Monaco's Kylian Mbappe.
Lyon have signed full-back Fernando Marcal from Benfica for €4.5 million, the Ligue 1 club has confirmed.
The fixture list for Paris Saint-Germain looks gentle to start so they'll need to take advantage before their meetings with champions Monaco.