The Cottagers attempted to sign the former Liverpool keeper on transfer deadline day in January, but there was not enough time to complete the deal.
Dutch newspaper Voetbal International reports that the Premier League club are ready to return for the Bulgaria international.
With Mark Schwarzer nearing the end of his playing days, Martin Jol is keen to sign another goalkeeper to provide competition for David Stockdale, who is set to return from a loan spell at Hull City.
The Dutch coach has a very high opinion of Mihaylov and is planning to add him to his ranks in the summer transfer window.
The 24-year-old, who joined Twente on a free transfer from Liverpool, has made a total of 84 Eredivisie appearances for the Tukkers and is currently regarded as one of the best goalkeepers in the elite division.