The Aston Villa forward pulled out of England duty last week ahead of the friendlies with Spain and Sweden, having been declared unfit for selection for the previous match against Montenegro.
Agbonlahor, 25, last featured for England in October 2009 and time is running out, with just one friendly remaining in February, possibly against Holland, before Capello names his provisional squad for Poland and Ukraine.
But McLeish believes the in-form forward, who has scored five times this term and is expected to be fit for Monday’s trip to Tottenham, can still force his way into Capello’s plans.
McLeish said: “There are a couple more games. Fabio Capello has got the door open. I don’t think he has got the door closed on anybody. It’s just a shame that after Gabby turned up and trained he got the injury, but the England camp were adamant he needed to come back.
There are a couple more games
“They did a scan on him and flagged up the nick on his hamstring.
“I’m sure he is disappointed because he saw a wee chink of light that he’d possibly get some playing time. He went in good faith and unfortunately came back with this little problem. But he’s still young and still has opportunities if he continues to play at the level he’s playing for us.
“Gabby’s certainly got a lot to give for England. We want Gabby to maintain the form he’s in to catch Capello’s eye, hopefully for the European Championships.”