Chairman Ray Ranson travelled to Glasgow yesterday and is having talks with both players today.
Speaking to the CT,Chris Coleman said: "Wrighty has been fantastic and it will be great to get him signed up. We hope to get that done by the weekend.
"Clinton is slightly different - we have not quite agreed yet but we would love to get him.
"We've got to be careful with him because he's not trained a lot and if he gets injured in a game when he's not under contract, who's going to sign him?
"If it all happens we will be looking to get a couple of games going next week - even then he wouldn't be ready to start against Norwich, but he might be able to come off the bench."