migrate swift version 3 to 4

What is the version of XCode ?

If recent, it can probably only convert from Swift 4 to Swift5.

You need older XCode (10.x) to convert to Swift4.

The version of xcode is 10, but the project does not appear in the migration option. I want to know why.

Probably because the project doesn't match the criteria for conversion. Are you sure it is not already a Swift 4 project ?

Do you see some messages in the Issue Navigator (left panel), such as:
Swift Conversion Group
Conversion to Swift 5 is available

Validate Project Settings Group
xxxxxxxApp.xcodeproj Update to recommended settings

If so, use those to update.

the project does not appear in the migration option. I want to know why.

One possibility is there are no targets with Swift Language Version set to Swift 3.
Have you checked the Build Settings of all the targets in your project?

I installed the latest version of xcode and tried to open the project's work area and an alert appeared saying that I would need to migrate to version 4.x, because the current one is in 3.x and for that I would need to download version 10 of xcode for migrate.

That was done.

But, in the errors / alerts panel, there is no such quick migration notification either (Edit menu -> Convert -> For the current Swift syntax)