Unable to connect on premise sql server from Sql Azure db
My suggestion is to gradually migrate databases from SQL Server on-premises to SQL Azure but keeping the original databases on-premises and have them synchronize with Azure using SQL Data Sync as explained here. You then will be able to access your databases on premises if you need without the latency of linked server or you can access them on SQL Azure if you want. 

Alternatively you can use replication as explained here.

Hope this helps.

Regards,

Alberto Morillo