Ralph Roberts, the firm's managing director, has already been to meet officials in Malta, although a formal tender process has yet to begin.
If successful in securing the contract McGill's, based in Greenock and owned by Rangers investors Sandy and James Easdale, would effectively double in size.
The opportunity has come about as Malta Public Transport Services, which is owned by the Maltese government, signed a deal to take over the bus operations from Arriva at the start of this year. Arriva was just 30-months into a 10-year contract to provide bus routes around the island when it decided to exit.
Now the Maltese government is expected to ask for expressions of interest from potential new operators in the next few weeks before a full tender document is released later.
A new operator could be named before June.
Mr Roberts, who worked at Arriva before joining McGill's in 2012, said: "We want to grow but [acquisition] opportunities in the UK are difficult.
"Malta would double us in size but that is something we can cope with."
Mr Roberts said Malta Public Transport Services employs around 1000 people, compared to 700 at McGill's, but, at 360, has a similar number of buses. He believes if McGill's is able to secure the tender the company would be able to move from a subsidised bus service to making the market in Malta "largely commercial" in three to five years.
Mr Roberts, who has worked in Europe for Arriva and also in a previous role at Rentokil, confirmed McGill's will submit an expression of interest unless there is anything "outlandish" in the demands from the Maltese government.
McGill's, which operates more than 40 routes in Inverclyde, Renfrewshire and East Renfrewshire, reported a £659,404 pre-tax profit in annual accounts for 2012.