Since the militant attack, which killed six policeman and a driver, Pakistan have played most of their 'home' matches in the United Arab Emirates.
Pakistan Cricket Board president Shaharyar Khan expects Zimbabwe to play in Lahore and Karachi in mid-May.
He added that Zimbabwe will assess security before confirming the matches.
Khan said his Zimbabwe counterpart, Wilson Manase, had explained the plans during a meeting of the International Cricket Council in Dubai last week.
"He told me they are coming with their full team, but for a week," said Khan.
If the tour goes ahead, Zimbabwe will be the first Test-playing nation to return to Pakistan, although Afghanistan and Kenya - neither of whom have Test status - have toured the country since the attack on low-profile series.
Pakistan are set to host top-level cricket for the first time since the 2009 gun attack on the Sri Lanka team bus, with Zimbabwe lined up to tour.