The El Niño–Southern Oscillation (ENSO) teleconnection to Europe is projected to strengthen under global warming in most climate model simulations. However, given the current difference between recent observations and historical model simulations of tropical Pacific sea surface temperature trends, with models simulating an El Niño‐like warming in recent decades which is in disagreement with observations, it is important to understand the relative contributions of changes to the teleconnection forcing and background state to the overall teleconnection change. Using idealized climate model experiments, we show that both the eastward shift of El Niño precipitation and background state changes make contributions to the overall teleconnection change. These results suggest that the ENSO–Europe teleconnection can be expected to strengthen under global warming, even if ENSO precipitation anomalies do not shift eastwards as currently projected. However, the magnitude of the strengthening may depend on how much of an eastward shift does occur.