The Portugal international has not started as many games as he wanted so far this season.
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Veiga, who can play in central defense, central midfield, and at left-back, has featured seven times in the Premier League this season.
Per The Mirror, Bundesliga outfit Stuttgart are showing interest in doing a loan deal.
Italian giants Napoli are also serious about bringing him in on a temporary deal.
Veiga has been a regular in the Conference League for Chelsea but knows that coach Enzo Maresca will field stronger teams in the latter stages of that competition.