Crystal Palace are reported to have paid £10 million for Wickham, who was previously on loan at Leeds United.
The Bristol City CEO, Mark Ashton, has already expressed an interest in landing Nketiah, should Arsenal recall the 20-year-old in January.
And the newspaper claims the Robins have now held initial talks about a January deal for Wickham, who played for Leeds on a temporary basis earlier this decade.
The 26-year-old has barely featured for Crystal Palace, who are reported to have paid £10 million for him in 2015, since he suffered a serious knee injury in November of the following year.
And Palace are said to be open to offers, with Watford and Nottingham Forest also being credited with an interest.
Bristol City have emerged as rivals to Leeds' promotion bid this season and have done so largely in the absence of Benik Afobe, the on-loan Stoke City striker who scored three goals in five games before suffering a serious knee injury of his own.
And the addition of one - if not two - new striker(s) this winter could give the Robins' Premier League aspirations a significant shot in the arm.
The Bristol Post states that: "Unless there is a dramatic shift in his playing time at Elland Road, Nketiah will return to north London and the Gunners will seek a new loan destination, although City are one of several clubs keen on taking the striker until summer 2020."
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