Tranmere have offered contracts to midfielder James Rowe and striker Shaun Jeffers after successful trial spells.
Rowe, who played 42 times for Forest Green last season, began his career with Reading and Southampton.
Jeffers, 21, spent five season on the books of Coventry with loan spells at Cheltenham and then most recently Tamworth last season.
Manager Ronnie Moore told Wirral News: "We have made offers to Rowe and Jeffers. Now it is up to them whether they take up those offers.
"They are young players and they are having a chat with their parents. I think they both have a bright future in the game.
"I think Rowe is going to be a player and there's plenty to come from Jeffers up front. If we can nail them both we would like to do it."