With Celtic Park being used for the opening ceremony of the Commonwealth Games on July 23, the pitch will be out of use for the first qualifiers.
Murrayfield is one of the likely options for Celtic, but the Parkhead chief executive also said there are other options for the club, most notably in Dublin or the north of England.
Hampden and Ibrox are also being used for the Commonwealth Games so were never in the running as options.
"We are currently in discussion with Uefa in terms of what options we have," said Lawwell. "Once they are happy with those options we will speak to the relevant owners of the stadia.
"There are other options to Murrayfield, probably less likely, but there are other options we can't let you know about yet, possibly outside Scotland.
"There is an angle there we could maybe look at, but again we need Uefa's approval.
"It could be England or Ireland. The Aviva in Dublin or Croke Park or maybe even down south at a northern Premiership club.
"We have a big support in Dublin and the stadium was full when we played Liverpool in the summer there.
"It's a list of three or four, maybe five. We look at that internally and then when we come up with a preferred three we will take it forward.
Uefa would have to give Celtic approval to play the games outwith their own country, and Lawwell will also consult Neil Lennon too before a final decision is made.
"Neil would have an impact on the decision," he said. "And we would need to look at ways of making sure the atmosphere was there and it was well attended.
"Murrayfield is a big attraction clearly because it is near for the supporters, it's a fantastic stadium. It would be a high contender. We will probably reach a decision early in the New Year so we can make a plan."
Yesterday's announcement regarding Celtic Park as the venue for this season's Scottish Cup final has caused a stir among some supporters, with social media sites endlessly debating the timing of the decision.
The SFA were quick to point out the planning necessary to arrange games of the magnitude of the cup final, but it is fair to suggest that further debate will be forthcoming nearer the time, especially should Celtic make the final.
Furthermore, should it transpire the William Hill Scottish Cup Final is the stage for the first Old Firm game since Rangers went into administration, there would be much made of the fact Celtic hold home advanatge. Any ticket split will have to be 50-50 but if it does come to an Old Firm meeting, Lawwell has no fears about any problems that may arise.
He said: "If that's the way it turns out, that's the way it turns out. It's going to happen sometime. The next one will create a high level of interest in Scotland and, I'm sure, worldwide."
Lawwell is also not overly concerned about further interest from clubs in goalkeeper Fraser Forster.
Celtic rebuffed an approach from Benfica this summer, but given his form it is inevitable another club will come in for him.
"These things sort themselves out," said Lawwell. "If we are offered the right fee we will take it and reinvest it in another goalkeeper or another centre forward or another midfielder.
"But also within that equation if a player is trebling or quadrupling his wages, then it's an easy decision for him.
"So there's no real friction preventing that happening. The player is happy, the club - for the right fee - is happy and the buying club is happy.
"No matter what we do there is a realisation that in a very short period of time, the next-door market can pay huge amounts of money that we could never compete with."