Thanks for posting your query in Q&A.
You can upgrade the pip, install all the dependencies and then publish to azure using remote build. Even though pip upgrading is being done on the local machine, it will make sure that the python project folder has updated its dependencies and then deployed to Azure Functions runtime.
Upgrade pip : python -m pip install --upgrade pip
Install dependencies : pip install -r requirements.txt
Publish to Azure : func azure functionapp publish <APP_NAME>