As an Early Bird player, Fields can be offered a contract that starts at 175% of his current salary or anything up to the average NBA salary (which is roughly $5 million). They can pay Fields this money without affecting their mid-level exception. However, if Fields just signs a one year deal for anything up to the average salary, then the following season the Knicks will have his full Bird Rights and then can re-sign him to a salary larger than the average salary. It really depends on how well Fields plays the rest of the year to determine what kind of deal he signs.
Lin, however, is not an Early Bird player since he has only played one year for the Knicks. Therefore, if they want to re-sign him, they would have to use one of the following:
1. The Non-Bird Exception, where they could pay him up to 120% of his current salary (or roughly $1 million)
2. The Bi-Annual exception (which is something like $2 million) or
3. However much of the mid-level (which is roughly $5 million) they would need to re-sign him