I have an offer from a company. The company say that they offer a relocation package which includes help with finding an apartment, and reimbursement for costs such as flight, luggage etc. There is no mention of relocation support for housing costs (i.e. rent, deposit). Is it okay to ask them if they can loan me the costs for the first month's rent? Or am I risking the offer being retracted by making them think I am not grateful they offered a relocation package?
Just be honest with them.
Tell them that you are very grateful for the opportunity and the help, and since you need to pay the new deposit before you will get the old one back you want to ask them to loan you some money.
This way, you make sure that they understnad that you are happy about the transfer and also explain why you need the money.