The 24-year-old has already agreed a three-year deal to join Robbie Neilson’s side but has faced a mountain of red tape as he bids to seal his switch from Israeli outfit Ashdod.
Hearts have lodged all the relevant paperwork at their end and the 17-times capped Oshaniwa is now waiting to hear whether the authorities have issued a visa to allow him to enter Scotland.
Hearts head coach Neilson wants to recruit Oshaniwa, who was linked with Celtic last January, to compete with Kevin McHattie for the left-back berth on their return to the Premiership.
Oshaniwa said: “I’ve been in constant touch with Hearts officials and they have been assuring me they are putting pressure on the British embassy to hasten up the process of issuing me a visa.
“We spoke on Wednesday morning, but you know this is not something you just get like that no matter the pressure.”
Speaking to Complete Sports, the Nigerian added: “I’ve been told it takes about ten working days to get the visa processed and if this is the case, then I’m expecting it to be ready on Friday this week.”
Hearts will continue their preparations for the new season tomorrow when they visit English Championship newcomers Preston North End. They round off their pre-season programme at home to Everton a week on Sunday, ahead of their Premiership opener at home to St Johnstone on 2 August.