The West Ham and former Everton manager is said to have watched Fredericks - whose Fulham contract expires in less than three months - in action last week.
And the report suggests he could be in luck, as the 25-year-old is keen to remain in London - the city in which he grew up.
Could Fulham's form throw a spanner in the works?
West Ham's alleged interest - and also that of Swansea - is said to pre-date much of Fulham's 20-game unbeaten run, which has seen them climb from 12th to second in less than four months.
And with promotion now likely for Slavisa Jokanovic's side, Fredericks may be tempted to snub other offers.
The Tottenham Hotspur academy product, who moved to Craven Cottage from Bristol City three years ago, was recently named in the Championship team of the season.
Will Moyes beat old club Everton, as well as Swansea and Fulham, to Fredericks' signature?