The Porto midfielder featured in his side's 2-0 loss against Benfica on Sunday night, with a Liverpool official reportedly in attendance.
Manchester United have also been heavily linked with the Brazilian, but Portuguese newspaper A Bola suggests Liverpool boss Brendan Rodgers is also keen on the 26-year-old.
The Anfield club sent an official to watch Fernando in the 2-0 defeat last weekend, ahead of a potential January bid for the midfielder.
Liverpool's Merseyside rivals Everton have also been mentioned as potential suitors, suggesting Fernando could be the subject of a transfer tussle later this month.
Rodgers and Moyes are both expected to be busy as the deadline nears, with both United and Liverpool keen to strengthen to consolidate a push for a top four spot in the Premier League.
The Brazil-born midfielder is eligible to play for Portugal after he was granted citizenship in December 2013, and he hopes to feature at the World Cup this summer.
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