Ice Hockey UK - in conjunction with Dumfries and Galloway Council - hopes to host the under 20 and under 18 events at Dumfries Ice Bowl.
Proposals have been put forward to the International Ice Hockey Federation to stage the tournaments in 2018.
Voting on the bids is expected to take place on Friday to decide the venue for the competitions.
If successful, Dumfries would host under 20 division 2 group A and the under 18 division 2 group A.
It has previously staged a number of events including under 20 and under 18 world championship tournaments in the 2013/14 season and the women's division 2 group A tournament in 2015.
A double bid to bring some of the rising stars of ice hockey to Scotland is being made.