Trending @HCL; Need advice on getting job at the client payroll

I work in a MNC and the client that our team supports comes under fortune 10 companies. I have not received any hike in the past 2 years irrespective of getting multiple appreciation and getting things done within SLA and even getting escalated tickets resolved for the team.

I discussed with the manager but he isn't releasing me from project since I want to move to different role. He says I'm critical resource and the tower lead is not approving the release.

I want to know apart from looking outside, can I ask my client directly if they have any openings in a similar role? since I build a good repo with a few of my clients and they know my work very well. I want to know if anyone moved from company to client payroll? what do you guyz suggest?

PS: 8yoe and 15lpa