1994 XJ6 Trouble Starting

I have a 1994 XJ6, (91,000 miles) that after years of running fine, is now having difficulty starting. It does not seem to be a cold weather issue, nor does it matter if the car has been running for 30 minutes- it still takes multiple attempts before the engine will turn over (3-7 times). Once the car does turn over, it runs fine and I am not having any issues with the car shutting off or losing power. I've had the battery and starter checked and the air mass valve replaced, but the issue remains.

My mechanic now is suggesting that it's a fuel pump issue. Any thoughts?

Thanks in advance!