Both Bamba's and Antenucci’s futures at Elland Road are uncertain, with their contracts coming towards an end.
Bamba has just 18 months left on his current deal, while Antenucci’s contract expires in the summer.
Evans now wants to pair to force Massimo Cellino to make them offer to extend their stay in Yorkshire, by impressing between now and the end of the campaign.
“I’ve said to Mirco and Sol to go and have a good, special end to the season and make it the case that someone has to come to you with an offer, whether that be me or the president,” Evans said.
“Sol still has another year beyond this season, but we want him to finish this season really strongly.
“The same with Antenucci, when he’s on his game he’s a formidable striker and you’d certainly want him around, but he’s got to be a regular in the team to say that we want to give you longer.”
Bamba and Antenucci were both linked with Leeds’ exits in January, with interest rising in the pair.
Bamba and Antenucci’s next chance to impress Evans could come at the weekend, when Leeds take on Nottingham Forest.