Reports in Sunday newspaper The Sun claim that the Cottagers, who were relegated from the Barclays Premier League last season, are set to offer £2m for the Nottingham-born striker.
The London-based club are looking to alter their squad, having released several players over the past few days, in an attempt to return to the top tier of English football.
Fulham will return to the Championship (second tier) since 2001-02, when they were division champions with 101 points.
McGoldrick, who has attracted the attention of several Premier League clubs, has been out since mid-February due to a knee injury.
McGoldrick factfile:
1987- Born in Nottingham
2004- Joined Southampton from Notts County, where he was loaned out
2009- Joined Nottingham Forest for £1m
2011/12- Loaned out to Sheffield Wed and Coventry
2013- Joined Ipswich on loan, securing a permanent deal later that year