First, do you have experience interviewing other candidates? Unless you do the time to train you to interview is not right before you leave the company. There can be some liability if you should ask the wrong questions even though they may seem to be benign to you. So taking time to get you up to speed and for them to be confident in your abilities takes more of an investment than is wise to invest just to fill one position, especially if it is a standard job title that does not require some highly specialized knowledge to begin the work.
If you are already trained, thinking as a manager, the risk of potential problems outweighs any benefit you could have to the process. Most people providing extended lead time prior to leaving do so wanting to provide plenty of time to secure a replacement. But the reality of hiring is that unless the company is willing to pay 2 people for the same position for an extended period, the company will wait until it can extend and have an offer accepted to start in a relatively short period of time. This means that chances are the interviews for your position will likely happen about a month out from your departure. This perceived delay sometimes embitters the existing employee. I have provided plenty of time to secure my replacement but they wait until 3 weeks before I leave to start interviewing, there will be no time for me to train them! Those sorts of thoughts are understandable but the last thing your employer wants is to have to terminate you early because you acted unprofessionally in an interview.
Your manager likely already has a decent idea of what skills your position requires. If it was me I might run that skill list by you to see if you have any suggestions on improving it. I may have you meet someone that we are likely to extend an offer to, especially if you are going to be working with them for knowledge transfer for a week or so. But for the most part when you turned in your notice I am most concerned with you completing any tasks that are due before you leave, and with ensuring that what you have done is documented so that after you leave your absence is mitigated by complete and accurate documentation.