General Brazilian
prazo se aproximando / prazo chegando
Most common usage in Brazilian Portuguese
São Paulo
prazo fechando / prazo apertando
Informal expression commonly used in business contexts
Rio de Janeiro
prazo chegando / tá chegando o prazo
Casual, conversational usage
Portugal
prazo a aproximar-se / prazo a chegar
European Portuguese preference for gerund construction with 'a' + infinitive