“UEFA is aware of alleged terrorist threats made towards this week’s UEFA Champions League matches and is closely liaising with the authorities at the respective venues,” UEFA said in a statement.
“All matches are planned to go ahead as scheduled with appropriate security arrangements in place.”
There are two matches scheduled to be held in Madrid. Real Madrid hosts Manchester City on Tuesday and Atletico Madrid welcomes Borussia Dortmund on Wednesday.
Arsenal plays Bayern Munich in London on Tuesday and Paris Saint-Germain hosts Barcelona the following day.
French and Spanish ministers have said there will be enhanced security measures at the stadiums. Islamic State claimed responsibility for the attack on the Crocus Hall concert venue outside Moscow on March 22 in which 144 people were killed.
The return matches in the Champions League are scheduled for next week.