Azure SQL Managed Instance can support being a Subscriber from the following versions of SQL Server:
- SQL Server 2016 and later
- SQL Server 2014 RTM CU10 (12.0.4427.24) or SP1 CU3 (12.0.2556.4)
- SQL Server 2012 SP2 CU8 (11.0.5634.1) or SP3 (11.0.6020.0)
When your On-premises subscriber is on SQL Server 2008 R2, Azure SQL MI (publisher) can be SQL Server 2014 or lower.
The complete supportability matrix is here
Depending on the version of Managed Instance you require, you may have to upgrade your on-prem instance accordingly.
Although Azure SQL MI with the default compatibility level -140 (as of today) is backwards compatible, you can use Data Migration Assistant to determine if you really need to run your database in compatibility mode.
--
If an answer is helpful, please "Accept answer" or "Up-Vote" for the same which might be beneficial to other community members reading this thread.