Strauss has recently tried his hand at broadcasting during the Ashes series, but the former opening batsman has indicated that he could be prepared to leave the position to replace the outgoing Hugh Morris.
The 36-year-old told Sky Sports News: "One of the things that you've got to be very careful with when jobs like these become available is to understand the actual job properly.
"I've obviously seen Hugh Morris do parts of his job, but not the whole job.
"I'm looking into it, but they're decisions that need to made over the next couple of weeks, and I'll think quite long and hard about whether it's the right time and the right job for me."
The former Middlesex man retired from all forms of cricket in 2012.