Can I put moses basket in a cot? Is it safe?

My baby is 6 weeks old he's slept in a moses basket since birth. But he's outgrowing it. I was given a cot before he was born but we are planning on buying a new mattress for it in a few days. We are going to be putting up the cot today but Is it OK to put the moses basket in the cot and he still sleep in the basket( just for the few nights ) or do I have to keep it on a stand? Is it safe for it to be in the cot? I know it may seem a stupid question but I don't want to sleep him on a second hand mattress but we need to get the cot up ready.