The 36-year-old could become the oldest player in ATP Tour history to top the world rankings if he reaches the last four at the Rotterdam Open.
Rafael Nadal is not in action due to the fact he is recovering from an injury he picked up in the Australian Open last month.
But Federer could still have to get past fellow Swiss Stan Wawrinka in the quarter-finals if the duo get through their respective ties.
It would be another remarkable achievement just weeks after clinching his 20th Grand Slam title.
And Federer still can’t believe the success he has enjoyed over the past 13 months which has seen him win three major titles out of a possible five.
“It would be absolutely incredible,” Federer said.
“I can’t believe I’m this close, but No 1 has never been simple, never been easy to get there so I know it’s going to be a lot of hard work for me this week.
“Mentally, to cope with everything and also not thinking too far ahead because I’m not there yet.
“As long as you’re not world No 1, you’re not. It’s that simple.
“I think it would also mean a lot to my family, my team and my fans; everybody that has been so supportive along the way.
“My comeback since ’16 has been so incredible that we’re already happy as is but I thought I’d give it a go and see if I can get No 1 this week.”