What reagents can I use for the following transformation? I think this has something to do with formation of an iminium salt and reductive amination, but I'm not so sure.
Waylander is right - there's no reduction involved. Thioesters and amides are at the same oxidation state. Basically any "RCOX" compound where X is a heretoatom, is the same oxidation state as carboxylic acids. This includes esters and acid chlorides.
Thioesters are particularly reactive, relative to esters and amides, so the reaction you've drawn will occur spontaneously at or close to room temperature by treatment with methylamine without other reagents or catalysts. In esters and amides, the O or N (respectively) lone pair overlaps very effectively with the carbonyl π-bond. Attack by a nucleophile would disrupt this conjugation, so esters and amides often need harsh conditions or catalysts to react with weak to moderate nucleophiles. In contrast, the S atom lone pair of a thioester does not overlap as effectively, due to longer C–S bond length and size difference between carbon 2p orbital and sulfur 3p orbital.