Celtic Park is out of action due to the Commonwealth Games in Glasgow and so matches will move across the Central Belt to Edinburgh.
Lawwell said: "Clearly we very much hope to be involved in the Champions League qualifying matches in July and early August and if this is the case then we felt it important that our fans know our proposed arrangements as early as possible.
"We are fortunate that we have such a fantastic and sizeable support and clearly it is important that we allow as many fans as possible to attend our matches.
"Murrayfield is a magnificent stadium, it is the obvious choice and we are sure it will be a venue which will provide a great footballing occasion.
"We will keep our supporters well informed of all potential arrangements as we move forward".
Scottish Rugby's Director of Commercial Operations, Communications and Public Affairs, Dominic McKay, said: "We're delighted to welcome Celtic Football Club to Murrayfield for their Uefa Champions League qualifying matches this summer, one of the biggest annual sport competitions.
"Scottish Rugby is proud of the facilities we have on offer in Edinburgh. This is a fantastic opportunity for Celtic to work with us to promote Murrayfield as a venue not just for rugby, in 2014."