Constructors cannot move unto a starbasetile, because they will always prompt an upgrade. However, that doesn't sound like it's your problem:
Is the Starbase yours? You might want to check this, because if it is, you should be able to send your contructor towards it (you can set the starbase as its destination, but it will only then refuse to move unto the tile, instead prompting the upgrade screen).
You cannot move a fleet of yours unto a starbase that isn't yours. Trade-route minifreighters have no such problems, they can also occupy the same square as ships that aren't yours (or even hostile if the turnupdater moves them underneath a hostile ship)!
If a constructor refuses to upgrade, this can be because you forgot to add a constructor module (but in that case it should have no trouble occupying the same space as your starbase).