The Eagles boss is unsure if the ex-Spurs marksman will stay at Selhurst Park.
The former Arsenal and Tottenham Hotspur striker has impressed since signing a six-month deal with the Eagles in January, netting once in four games to remind the Premier League of his talent.
The 31-year-old had his contract terminated by Spurs back in September, though the North London club have continued to pay his £100,000-a-week salary.
Adebayor is no stranger to controversy and has had his behaviour questioned throughout his 10-year spell in England, but Pardew has hailed his conduct and says a decision will be made over his long-term future when the season finishes.
“I think this is a question which is probably going to come up between now and the end of the year,” he told reporters at a press conference, via the Daily Mirror. “I think I am quite clear in my mind about it – it is an open book really for Ade and for us.
"We will run with each other till the end of the year and then decide what we want to do. His decision will be just as important as ours because he is a big-name player and this isn't a big-name club.
"It is a Premier League club, growing, but we will have to have that conversation at the end of the season. So far, his personality and his conduct around the training ground has been of the highest order."
The Togo marksman joined Arsenal from Monaco in 2006, before sealing a £25 million move to Manchester City in 2009.
He ultimately fell out of favour under manager Roberto Mancini, who loaned him to Real Madrid and then the Lilywhites for the 2011-12 campaign, before making the move permanent the following summer.
Adebayor will hope to continue impressing for Palace in Saturday's evening visit to West Bromwich Albion.