When someone asks you for something, it's a "request". When you think about whether to say "yes" or "no", you're "considering" the request.
The phrase "consider a request" is slightly formal.
Other things that you can "consider" include:
consider doing something
I considered going into medicine, but I decided that I wanted to do something a little more creative.
- consider an offer
- consider the options
- consider the consequences (of doing something)
I don't think she's really considered the consequences of taking on such a huge responsibility.