The 23-year-old joined the Italian club with huge expectations but he has not been able to fulfil his potential with them so far.
It is believed that Roma could cash in on the winger if a reasonable offer comes in this summer.
It will be interesting to see if the two Premier League clubs come forward with a concrete offer for Under now.
The Turkish winger is quite talented and he has a big future ahead of him. A move to Leicester or Newcastle could give him the platform he needs to fulfil his potential.
Regular first-team football in the Premier League would help him develop as a player and he is likely to be tempted to make the move if there is a concrete proposal on the table.
According to reports (h/t sportwitness), Roma are looking for a fee of around €25 million for Under but Newcastle are only looking at a loan deal.
It will be interesting to see if they can convince the Italian outfit to loan the player to them the season.
Newcastle need to add some quality and depth to their wide attacking options an under would be a really useful option for them.