We want to integrate Circle CI with salesforce for deployment, but the project is not sfdx project. Means the project structure which we have is like below :
-Main
-src
-classes
-triggers
-manifest
-package.xml
Can we use the same above project to integrate with circle CI or do we need to create an another sfdx project?
CircleCI doesn't know anything about Salesforce. It's just a CI harness for any build system. (There are some orbs for SFDX that may help in your implementation, though).
You will presumably be using (you should be using) the SFDX CLI as your deployment tool inside your CircleCI jobs. SFDX can deploy both Metadata API-format source, as shown here, and Salesforce DX-format source. You'll simply need to include the appropriate commands (such as sfdx force:mdapi:deploy) in your build scripts.
The position of your package.xml in a separate manifest directory is unfamiliar to me in a Metadata API-format project, but this is easy to change in a script if needed too.
