Griffiths fired his first senior treble to inspire Hibs' 4-2 cup win at Kilmarnock on Sunday which saw them through to the last four.
The 22-year-old striker, who earned his first Scotland cap under caretaker boss Billy Stark in the 2-1 friendly win over Luxembourg in November, is hoping to be recalled for the World Cup qualifying double-header against Wales and Serbia later this month.
But Griffiths knows Strachan, who took over in January, has a lot of talent to choose from up front.
"It would be an absolute dream if I was called up and would top off a great month for me," the frontman, who has scored 22 goals this season, told the Daily Record.
"But the manager picks the squad and there are a lot of great strikers out there to choose from.
"Guys like Steven Fletcher and Jordan Rhodes are regularly banging in goals in the Premiership and Championship. So I will just keep my head down and try to score my goals for Hibs.
"If that gets me international recognition, fine. If not, I'm not going to be too disappointed.
"I'm certainly not thinking he can't overlook me."