The 20-year-old is out of contract at Coventry this summer, leaving Leicester to negotiate a compensation package with the League Two side.
Leicester made a formal offer of roughly £300,000 on 1 July and are expected to go back this week, after returning from Hong Kong, with a second offer closer to the £500,000 that Coventry are hoping for.
Leicester have proven to be the team most willing to pay a serious fee for the man who scored for Coventry in the EFL Trophy final win over Oxford United.
Swansea City had been the initial favourites to sign the Wales Under-20 international, but chairman Huw Jenkins baulked at paying close to £500,000 for someone who has never played at higher than League One level.
Newcastle United and Brighton were also keen on Thomas but Leicester have been more enthusiastic about signing him than anyone else.
Thomas would likely be loaned out for the forthcoming season.
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