The traditional Tuesday and Wednesday slot used by Uefa will be set aside as the first leg coincides with the 'Twelfth' marches in Northern Ireland.
It's understood the new date has been agreed by the clubs and approved by the Police Service of Northern Ireland.
Linfield must first defeat La Fiorita of San Marino in a first-round clash.
The Northern Ireland champions will host La Fiorita in Belfast on 28 June, with the return leg on 4 July.
If the Blues progress they will play the 1967 European Cup winners, who are managed by County Antrim-born Brendan Rodgers, for the first time.
The first leg of the Champions League second round qualifiers are scheduled to take place on 11/12 July.
However they are key dates in the annual Orange celebrations, sparking fears of trouble with Celtic's large travelling support heading to Belfast at the height of the marching season.
Linfield's national stadium is located in the largely loyalist Sandy Row area.
Police are understood to have ruled out the match taking place on either the 11th or 12th amid concerns tensions could erupt between Celtic and Linfield fans.
A possible solution to the dilemma would have been to switch the ties, with Celtic hosting the opener in Glasgow before the return a week later.
Linfield dismissed that possibility as they look to cash in on the right to host the all-important first leg, Blues chairman Roy McGivern telling BBC Sport a home leg first was always "the preferred choice" of the Irish Premiership champions.
Celtic defeated Irish League opposition in Belfast four years ago with a 3-0 win over Cliftonville in a Champions League qualifier.
Celtic's potential Champions League qualifier with Irish Premiership champions Linfield has been pencilled in for Friday 14 July at Windsor Park.