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.