Parker wants to strengthen his defence as well, and Fulham are considering a loan move for their former player Ryan Sessegnon, who left Craven Cottage for Tottenham last summer in a £25m deal, but who has not played a minute of football under Jose Mourinho since the re-start.
Kyle Walker-Peters, who was on loan at Southampton from Spurs last season, is another candidate.
The Cottagers have also been linked with a move for ex-Chelsea defender Branislav Ivanovic, now a free agent after leaving Zenit St Petersburg.
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