Scharner is currently at German side Hamburg.
"Over the next 48 hours I am hoping to bring one or two players in and Paul is one of them," Martinez said.
"Paul could be a perfect replacement because he knows the football club and the Premier League.
"He is someone who could fit in at centre-half and with the way we play.
"The fans would welcome him with open arms and it is something that I am hoping to have positive news on over the next 48 hours."