West Brom rejected multiple bids for Evans, whose contract expires in 2019, in the previous transfer window, including one from league leaders Manchester City, and Pardew fears that further offers could pave the way for his departure.
'Jonny's dealt with it in his way.
Evans will now face a hard choice going into the second half of the Premier League season, with the option of becoming a squad player at runaway leaders Manchester City - or remaining with first team football elsewhere.
Boss Pardew said: "Do I want to lose him?"
"Jonny Evans is certainly one of them, and he's our captain". Course not. Do I fear losing him? Of course I do'.
Arsenal boss Arsene Wenger, meanwhile, will see Per Mertesacker retire at the end of the current campaign.
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Pardew, who took charge of his first Albion match against Crystal Palace following the dismissal of Tony Pulis, tried to sign Evans when he was Newcastle manager.
The Baggies now sit just above the relegation zone in the Premier League table having recorded three successive draws, with a visit to bottom-of-the-table Swansea coming up on Saturday.
The need for another central defender was further exacerbated last month when John Stones was ruled out for up to six weeks with a hamstring injury suffered during the 2-0 win at Leicester.
'We need to win at least nine games to be safe and hopefully after Saturday it'll be eight games'.