Former Rovers midfielder Wellens rejoined the South Yorkshire club on a short-term contract in the summer after leaving Leicester by mutual consent.
That deal is set to expire in four weeks' time but Dickov is keen to keep the 33-year-old at the Keepmoat Stadium.
"That (a new contract for Wellens) is something we're looking at," Dickov told BBC Radio Sheffield. "He wants to stay and we want him to stay.
"If I wasn't optimistic about him staying then I wouldn't have made him my captain."
Wellens agreed a two-year contract with Doncaster pending Sequentia Capital's proposed takeover of the club but the board of directors at Rovers opted to turn down the Irish-led consortium's investment offer.
He has made 18 appearances in all competitions this season for Dickov's team.